# Research Reports

Here is a list of publications and preprints, categorized as follows.

there is also an associated list of research report abstracts, including links by theme and (some) illustrative pictures. Preprints are early pre-publication versions: each preprint title “Research Report XXX” is linked to the corresponding abstract. Some preprints can be downloaded in *gzipped PostScript* form (here is information on how to deal with gzipped files) or as Acrobat PDF : in such cases appropriate icons link to the corresponding files. To obtain paper copies of those preprints without links, contact our departmental secretary. Further icons link to final publication versions as follows:

Titles of articles published in free electronic journals are linked to the relevant web-page.

Please also check out the preprints written by my colleague Elke Thönnes.

Readers of my *Mathematica* Journal article, *Stochastic Integrals and their expectations*, may download the associated software from this link: itointegral.zip [65k].

## Unpublished research reports and DPhil Thesis (most recent outputs come first)

Rubber Bands, Pursuit Games and Shy Couplings |
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Dynamic Filtering of Static Dipoles in MagnetoEncephaloGraphy |
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“Constructing Markov chains for differentiable curves” University of Warwick Department of Statistics Research Report 409 (2004) |
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“Simplification rules for Ito Integral” University of Warwick Department of Statistics Research Report 410 (2004) |
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“Perfect implementation of simulation for conditioned Boolean Model via correlated Poisson random variables” (co-authored with Y. Cai); University of Warwick Department of Statistics Research Report 350 (1999) |
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“Perfect simulation of point processes using Metropolis-Hastings algorithms” (co-authored with J. Møller); University of Warwick Department of Statistics Research Report 347 (1999) |
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“Perfect implementation of a Metropolis-Hastings simulation of Markov point processes” (co-authored with J. Møller); University of Warwick Department of Statistics Research Report 348 (1999) |
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“Itovsn3 in AXIOM: modules, algebras and stochastic differentials” University of Warwick Department of Statistics Research Report 328 (1998) |
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“Stochastic calculus in Mathematica: software and examples” University of Warwick Department of Statistics Research Report 333 (1998) |
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“Computer algebra and yoke geometry I: When is an expression a tensor?” University of Warwick Department of Statistics Research Report 237 (1992) |
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“An animated tour of the Brownian path (Brownian motion and computer algebra)” University of Warwick Department of Statistics Research Report 247 (1992) |
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“Symbolic Itô calculus: An introduction” University of Warwick Department of Statistics Research Report 217 (1991) |
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“Some Problems of Probability Theory” (DPhil Thesis) Department of Mathematics, University of Oxford (1979) |

## Books (most recent outputs come first)

New Perspectives in Stochastic Geometry (co-edited with I. Molchanov); |
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Markov chain Monte Carlo: Innovations and Applications (co-edited with F. Liang, J.-S. Wang); World Scientific (2005) |
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Stochastic Geometry: Likelihood and Computation (co-edited with O. E. Barndorff-Nielsen, M. N. M. van Lieshout); Chapman and Hall / CRC (1999) |
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New Directions in Dirichlet Forms (co-authored with J. Jost, U. Mosco, M. Röckner, K. T. Sturm); American Mathematical Society (1998) |
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Stochastic geometry and its applications (co-authored with D. Stoyan, J. Mecke); John Wiley & Sons (1995) Now available in paperback, October 2008. |
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Networks and Chaos - Statistical and Probabilistic Aspects (co-edited with O. E. Barndorff-Nielsen, J. L. Jensen); Chapman and Hall (1993) |

## Journal and other publications (most recent outputs come first)

“Fibre-generated Point Processes and Fields of Orientations” (co-authored with B. J. Hill and E. Thoennes), |
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“Shy Couplings, CAT(0) Spaces, and the Lion and Man” (co-authored with M. Bramson and K. Burdzy), Annals of Probability, to appear arXiv:1007.3199. |
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“Limit theorems for empirical Fréchet means of independent and non-identically distributed manifold-valued random variables” (co-authored with H. Le), Brazilian Journal of Probability and Statistics, (2011) 25(3), 323-352arXiv:1102.0228. |
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“Geodesics and flows in a Poissonian city”, Annals of Applied Probability (2011) 21 (3) 801-842. Also arXiv:0910.5115 |
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“Statistical Shape Theory” (co-authored with H. Le). In New Perspectives in Stochastic Geometry, Oxford University Press, 2010, pp 348-373 | ||

“Networks and Poisson line patterns: fluctuation asymptotics” in Oberwolfach Reports, (2008) 5 2670-2672. |
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“Brownian couplings, convexity, and shy-ness”, Electronic Communications in Probability (2009) |
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“Short-length routes in low-cost networks via Poisson line patterns” (co-authored with D. J. Aldous). Advances in Applied Probability (2008) 40 (1) 1-21. |
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“Perfect Simulation for a Class of Positive Recurrent Markov Chains” (co-authored with S. B. Connor). |
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“Coupling all the Lévy stochastic areas of multidimensional Brownian motion”. |
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“Confidence bands for Brownian motion and applications to Monte Carlo simulation” (co-authored with J. Marin, C. P. Robert). Statistics and Computing (2007) 17: 1-10 (also in previous form in 2005 as “Brownian confidence bands on Monte Carlo output”, University of Warwick CRiSM Research Report 05-2) |
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“Stochastic Integrals and their expectations” Mathematica Journal (2005) 9 |
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“Notes on Perfect Simulation” (co-edited with F. Liang, J.-S. Wang). Markov chain Monte Carlo: Innovations and Applications (2005) pp 93-146 (also University of Warwick Department of Statistics Research Report 428) |
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“Geometric Ergodicity and Perfect Simulation”. Electronic Communications in Probability (2004) 9:140-151 (also University of Warwick Department of Statistics Research Report 427) |
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“Coupling Iterated Kolmogorov Diffusions” (co-authored with C. J. Price). Electronic Journal of Probability (2004) 9:382-410 (also University of Warwick Department of Statistics Research Report 416) |
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“Ising models and multiresolution quad-trees” (co-authored with R. G. Wilson). Advances in Applied Probability (2003) 35:96-122 (also University of Warwick Department of Statistics Research Report 402) |
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“Bayesian analysis of vascular structure” (co-authored with E. Thönnes, A. Bhalerao, R. G. Wilson). LASR 2003 (2003) To appear |
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“Book review: Statistics of the Galaxy Distribution, by Martínez and Saar”. Journal of the American Statistical Association (2003) 98:248 |
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“Simulation of cluster point processes without edge effects” (co-authored with A. Brix). Advances in Applied Probability (2002) 34:267-280 (also University of Warwick Department of Statistics Research Report 382) |
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“Perfect simulation for correlated Poisson random variables conditioned to be positive” (co-authored with Y. Cai). Statistics and Computing (2002) 12:229-243 (also University of Warwick Department of Statistics Research Report 349) |
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“Small sets and Markov transition densities” (co-authored with G. Montana). Stochastic Processes and Their Applications (2002) 99:177-194 (also University of Warwick Department of Statistics Research Report 371) |
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“A Bayesian approach to inferring vascular tree structure from 2D imagery” (co-authored with E. Thönnes, A. Bhalerao, R. G. Wilson); Proceedings IEEE ICIP-2002 (2002) II:937-939 (also University of Warwick Department of Statistics Research Report 391) |
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“Symbolic Ito calculus: an ongoing story” Statistics and Computing (2001) 11:25-35 (also University of Warwick Department of Statistics Research Report 327) |
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“Gambling with the truth: Markov chain Monte Carlo” Challenges for the 21st Century: ICFS Mathematics and Theoretical Physics, Singapore March 2000 (2001) pp 83--101 |
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“Inferring vascular structure from 2D and 3D imagery” (co-authored with A. Bhalerao, E. Thönnes, R. G. Wilson); Medical Image Computing and Computer-Assisted Intervention, proceedings of MICCAI 2001 (2001) 2208:820-828 (also University of Warwick Department of Statistics Research Report 392) |
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“Efficient Markovian couplings: examples and counterexamples” (co-authored with K. Burdzy); The Annals of Applied Probability (2000) 10:362-409 (also University of Warwick Department of Statistics Research Report 331) |
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“Stationary countable dense random sets” Advances in Applied Probability (2000) 32:86-100 (also University of Warwick Department of Statistics Research Report 341) |
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“Gambling with the Truth: Markov chain Monte Carlo” Mathematical Medley (2000) To appear |
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“Perfect simulation using dominating processes on ordered state spaces, with application to locally stable point processes” (co-authored with J. Møller); Advances in Applied Probability (2000) 32:844-865 (also University of Warwick Department of Statistics Research Report 347) |
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“Zeros of Brownian Polynomials” (co-authored with C. J. Price); Stochastics and Stochastic Reports (2000) 70:271-308 (also University of Warwick Department of Statistics Research Report 353) |
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“Riemannian barycentres and geodesic convexity” (co-authored with J. M. Corcuera); Math. Proc. Camb. Phil. Soc. (1999) 127:253-269 (also University of Warwick Department of Statistics Research Report 325) |
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“Geometry, statistics, and shape” Geometry in Present Day Science (1999) pp 143-163 (also University of Warwick Department of Statistics Research Report 319) |
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“Quermass-interaction processes: conditions for stability” (co-authored with M. N. M. van Lieshout, A. J. Baddeley); Advances in Applied Probability (1999) 31:315-342 (also University of Warwick Department of Statistics Research Report 293) |
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“Perfect Simulation in Stochastic Geometry” (co-authored with E. Thönnes); Pattern Recognition (1999) 32:1569-1586 (also University of Warwick Department of Statistics Research Report 323) |
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“From Stochastic Parallel Transport to Harmonic Maps” (co-authored with J. Jost, U. Mosco, M. Röckner, K. T. Sturm); hrefhttp://www.ams.org/bookstore?fn=20&arg1=amsipseries&item=AMSIP-8 (1998) pp 49-115 (also University of Warwick Department of Statistics Research Report 321) |
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“Perfect simulation for the area-interaction point process” Probability Towards 2000 (1998) pp 218-234 (also University of Warwick Department of Statistics Research Report 292) |
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“Computer Algebra” Encyclopedia of Biostatistics (1998) 1:839-845 (also University of Warwick Department of Statistics Research Report 301) |
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“A diffusion model for Bookstein triangle shape” Advances in Applied Probability (1998) 30:317-334 (also University of Warwick Department of Statistics Research Report 296) |
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“On some weighted Boolean models” Advances in Theory and Applications of Random Sets (1997) pp 105-120 (also University of Warwick Department of Statistics Research Report 295) |
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“Perfect Simulation for Spatial Point Processes” Bulletin ISI, 51 (1997) ^{st} session proceedings, Istanbul (August 1997)3:163-166 (also University of Warwick Department of Statistics Research Report 308) |
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“Gromov’s hyperbolicity and Picard’s little theorem for harmonic maps” (co-authored with M. Cranston, Yu. Kifer); Stochastic Analysis and Applications, Gregynog, (9 (1996) pp 139-164 ^{ th}-14^{ th} July 1995)(also University of Warwick Department of Statistics Research Report 280) |
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“Coupling constructions for hypoelliptic diffusions: Two examples” (co-authored with G. Ben Arous, M. Cranston); Stochastic Analysis: Summer Research Institute July 11-30, 1993 (1995) 57:193-212 (also University of Warwick Department of Statistics Research Report 261) |
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“The radial part of a Gamma-martingale and a non-implosion theorem” The Annals of Probability (1995) 23:479-500 (also University of Warwick Department of Statistics Research Report 231) |
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“Stochastic calculus, statistical asymptotics, strings and phyla” (co-authored with O. E. Barndorff-Nielsen, P. E. Jupp); Annales de la Faculté des Sciences de Toulouse Mathématiques (Série 6) (1994) 3:5-62 (also University of Warwick Department of Statistics Research Report 222) |
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“Probability, convexity, and harmonic maps II: Smoothness via probabilistic gradient inequalities” Journal of Functional Analysis (1994) 126:228-257 (also University of Warwick Department of Statistics Research Report 260) |
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“The radial part of Brownian motion II: Its life and times on the cut locus” (co-authored with M. Cranston, P. March); Probability Theory and Related Fields (1993) 96:353-368 (also University of Warwick Department of Statistics Research Report 244) |
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“Doing stochastic calculus with Mathematica” Economic and Financial Modeling with Mathematica (1993) pp 214-238 (also University of Warwick Department of Statistics Research Report 238) |
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“Computer algebra in probability and statistics” statistica neerlandica (1993) 47:9-25 (also University of Warwick Department of Statistics Research Report 236) |
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“On the empty cells of Poisson histograms” Journal of Applied Probability (1993) 30:561-574 (also University of Warwick Department of Statistics Research Report 239) |
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“Brownian motion and partial differential equations: From the heat equation to harmonic maps” Bulletin ISI, 49 (1993) ^{th} session proceedings, Firenze (August 1993)3:85-101 (also University of Warwick Department of Statistics Research Report 257) |
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“Limiting angle of Brownian motion in certain two-dimensional Cartan- Hadamard manifolds” (co-authored with E. P. Hsu); Annales de la Faculté des Sciences de Toulouse Mathématiques (Série 6) (1992) 1:169-186 (also University of Warwick Department of Statistics Research Report 216) |
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“A remark on the proof of Itô’s formula for C^{2} functions of continuous semimartingales” Journal of Applied Probability (1992) 29:216-221 (also University of Warwick Department of Statistics Research Report 202) |
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“Convex geometry and nonconfluent Gamma-martingales II: Well-posedness and Gamma-martingale convergence” Stochastics and Stochastic Reports (1992) 38:135-147 (also University of Warwick Department of Statistics Research Report 214) |
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“The Propeller: A counterexample to a conjectured criterion for the existence of certain convex functions” The Journal of the London Mathematical Society (Second Series) (1992) 46:364-374 (also University of Warwick Department of Statistics Research Report 213) |
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“Correction note to ‘Martingales on manifolds and harmonic maps’” (co-authored with H. Huang); Stochastics and Stochastic Reports (1991) 37:253-257 (also University of Warwick Department of Statistics Research Report 218) |
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“Symbolic Itô calculus: An overview” Probabilités Numeriques (1991) pp 186-192 (also University of Warwick Department of Statistics Research Report 223) |
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“Convexity and the hemisphere” The Journal of the London Mathematical Society (Second Series) (1991) 43:567-576 (also University of Warwick Department of Statistics Research Report 181) |
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“Convex geometry and nonconfluent Gamma-martingales I: Tightness and strict convexity” Stochastic Analysis, Proceedings, LMS Durham Symposium, 11th - 21st July 1990 (1991) pp 163-178 (also University of Warwick Department of Statistics Research Report 212) |
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“Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence” Proceedings of the London Mathematical Society (Third Series) (1990) 61:371-406 (also University of Warwick Department of Statistics Research Report 162) |
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“A spatial Markov property for nearest-neighbour Markov point processes” Journal of Applied Probability (1990) 28:767-778 (also University of Warwick Department of Statistics Research Report 172) |
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“The Euclidean diffusion of shape” Disorder in Physical Systems (1990) pp 203-217 (also University of Warwick Department of Statistics Research Report 161) |
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“Invited contribution to discussion of ‘A survey of the statistical theory of shape’ by D.G. Kendall” Statistical Science (1990) 4:111-113 |
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“Computer algebra and stochastic calculus” Notices of the American Mathematical Society (1990) 37:1254-1256 (also University of Warwick Department of Statistics Research Report 203) |
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“Coupled Brownian motions and partial domain monotonicity for the Neumann heat kernel” Journal of Functional Analysis (1989) 86:226-236 |
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“Diffusion processes” Applications of probability M343 (1988) |
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“Symbolic computation and the diffusion of shapes of triads” Advances in Applied Probability (1988) 20:775-797 |
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“Busemann functions and Brownian motion” Stochastic Calculus in Applications, Symposium Proceedings, Cambridge 1986 (1988) 197:63-68 |
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“Martingales on manifolds and harmonic maps” The Geometry of Random Motion (1988) 73:121-157 |
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“A summary of points raised in the Discussion Sessions” (co-authored with C. T. J. Dodson, P. E. Jupp, S. L. Lauritzen); Geometrization of Statistical Theory, Proceedings of the GST Workshop, University of Lancaster, 28-31 October 1987 (1987) pp 235-250 |
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“Stochastic differential geometry: An introduction” Acta Applicandae Mathematicae. An International Journal on Applying Mathematics and Mathematical Applications (1987) 9:29-60 |
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“The radial part of Brownian motion on a manifold: Semimartingale properties” The Annals of Probability (1987) 15:1491-1500 |
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“Computer algebra, Brownian motion, and the statistics of shape” Geometrization of Statistical Theory, Proceedings of the GST Workshop, University of Lancaster, 28-31 October 1987 (1987) pp 171-192 |
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“Discussion of read paper by Clifford, Green and Pilling” Journal of the Royal Statistical Society (Series B: Methodological) (1987) 49:286-287 |
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“Stochastic differential geometry” Proceedings, First World Congress of the Bernoulli Society (1987) 1:515-524 |
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“Mean values of stationary planar tessellations” (co-authored with J. Mecke); Journal of Applied Probability (1987) 24:411-421 |
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“Scattering processes and convergence to Brownian motion” (co-authored with M. Westcott); Advances in Applied Probability (1987) 19:81-105 |
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“A nonstandard proof of one of David Williams’ splitting-time theorems” (co-authored with N. J. Cutland); Analytic and Geometric Stochastics, Special Supplement to Advances in Applied Probability (1986) pp 37-47 |
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“Combinatorial Laplacians and isoperimetric inequality” (co-authored with J. Dodziuk); From local times to global geometry, control, and physics (1986) 150:68-74 |
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“Factorizations of Brownian motions and harmonic maps” (co-authored with K. D. Elworthy); From local times to global geometry, control, and physics (1986) 150:75-83 |
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“Stochastic differential geometry, a coupling property, and harmonic maps” The Journal of the London Mathematical Society (Second Series) (1986) 33:554-566 |
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“Nonnegative Ricci curvature and the Brownian coupling property” Stochastics and Stochastic Reports (1986) 19:111-129 |
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“Brownian motion in 4-space; is it tame?” Académie de la République Populaire Roumaine. Revue Roumaine de Mathématiques Pures et Appliquées (1985) 30:371-374 |
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“Brownian motion on 2-dimensional manifolds of negative curvature” Séminaire de Probabilités (1984) XVIII:70-76 |
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“Brownian motion and a generalised little Picard’s theorem” Transactions of the American Mathematical Society (1983) 275:751-760 |
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“Coupling methods and the storage equation” Journal of Applied Probability (1983) 20:436-441 |
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“Epidemics in competition II: The general epidemic” (co-authored with I. W. Saunders); Journal of the Royal Statistical Society (Series B: Methodological) (1983) 45:238-244 |
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“Contours and Baire category” The Bulletin of the London Mathematical Society (1982) 14:30-32 |
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“Bias in measurement of fission-track length distributions” (co-authored with G. M. Laslett, A. J. W. Gleadow, I. R. Duddy); Nuclear Tracks (1982) 6:79-85 |
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“Brownian motion, negative curvature, and harmonic maps” Stochastic Integrals, Proceedings, LMS Durham Symposium, 1980 (1981) 851:479-491 |
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“Contours of processes with multidimensional times” Proceedings, Sixth Conference on Probability Theory, Brasov, Romania (1981) pp 317-318 |
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“Contours of Brownian processes with several-dimensional times” Zeitschrift für Wahrscheinlichkeitstheorie und verve Gebiete (1980) 52:267-276 |
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“Alignments in two-dimensional random sets of points” (co-authored with D. G. Kendall); Advances in Applied Probability (1980) 12:380-424 |
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“The knotting of Brownian motion in 3-space” The Journal of the London Mathematical Society (Second Series) (1979) 19:378-384 |

If you want copies of any of the research reports then please mail or fax your requests to the departmental secretary.