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 prepublication 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 webpage.
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Unpublished research reports and DPhil Thesis (most recent outputs come first)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 

Dynamic Filtering of Static Dipoles in MagnetoEncephaloGraphy 

“Constructing Markov chains for differentiable curves” University of Warwick Department of Statistics Research Report 409 (2004) 

“Simplification rules for Ito Integral” University of Warwick Department of Statistics Research Report 410 (2004) 

“Perfect implementation of simulation for conditioned Boolean Model via correlated Poisson random variables” (coauthored with Y. Cai); University of Warwick Department of Statistics Research Report 350 (1999) 

“Perfect simulation of point processes using MetropolisHastings algorithms” (coauthored with J. Møller); University of Warwick Department of Statistics Research Report 347 (1999) 

“Perfect implementation of a MetropolisHastings simulation of Markov point processes” (coauthored with J. Møller); University of Warwick Department of Statistics Research Report 348 (1999) 

“Itovsn3 in AXIOM: modules, algebras and stochastic differentials” University of Warwick Department of Statistics Research Report 328 (1998) 

“Stochastic calculus in Mathematica: software and examples” University of Warwick Department of Statistics Research Report 333 (1998) 

“Computer algebra and yoke geometry I: When is an expression a tensor?” University of Warwick Department of Statistics Research Report 237 (1992) 

“An animated tour of the Brownian path (Brownian motion and computer algebra)” University of Warwick Department of Statistics Research Report 247 (1992) 

“Symbolic Itô calculus: An introduction” University of Warwick Department of Statistics Research Report 217 (1991) 

“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 (coedited with I. Molchanov); 

Markov chain Monte Carlo: Innovations and Applications (coedited with F. Liang, J.S. Wang); World Scientific (2005) 

Stochastic Geometry: Likelihood and Computation (coedited with O. E. BarndorffNielsen, M. N. M. van Lieshout); Chapman and Hall / CRC (1999) 

New Directions in Dirichlet Forms (coauthored with J. Jost, U. Mosco, M. Röckner, K. T. Sturm); American Mathematical Society (1998) 

Stochastic geometry and its applications (coauthored with D. Stoyan, J. Mecke); John Wiley & Sons (1995) Now available in paperback, October 2008. 

Networks and Chaos  Statistical and Probabilistic Aspects (coedited with O. E. BarndorffNielsen, J. L. Jensen); Chapman and Hall (1993) 
Journal and other publications (most recent outputs come first)
“Fibregenerated Point Processes and Fields of Orientations” (coauthored with B. J. Hill and E. Thoennes), 

“Shy Couplings, CAT(0) Spaces, and the Lion and Man” (coauthored with M. Bramson and K. Burdzy), Annals of Probability, to appear arXiv:1007.3199. 

“Limit theorems for empirical Fréchet means of independent and nonidentically distributed manifoldvalued random variables” (coauthored with H. Le), Brazilian Journal of Probability and Statistics, (2011) 25(3), 323352arXiv:1102.0228. 

“Geodesics and flows in a Poissonian city”, Annals of Applied Probability (2011) 21 (3) 801842. Also arXiv:0910.5115  
“Statistical Shape Theory” (coauthored with H. Le). In New Perspectives in Stochastic Geometry, Oxford University Press, 2010, pp 348373 

“Networks and Poisson line patterns: fluctuation asymptotics” in Oberwolfach Reports, (2008) 5 26702672. 

“Brownian couplings, convexity, and shyness”, Electronic Communications in Probability (2009) 14, Paper 7, 6680. Also arXiv:0809.4682 

“Shortlength routes in lowcost networks via Poisson line patterns” (coauthored with D. J. Aldous). Advances in Applied Probability (2008) 40 (1) 121.  
“Perfect Simulation for a Class of Positive Recurrent Markov Chains” (coauthored with S. B. Connor). Annals of Applied Probability (2007) 17 (3) 781808; see also "Correction. Perfect simulation for a class of positive recurrent Markov chains". Ann. Appl. Probab. (2007) 17 (56) 18081810 (also University of Warwick Department of Statistics Research Report 446) 

“Coupling all the Lévy stochastic areas of multidimensional Brownian motion”. Annals of Probability (2007) 35 (3) 935953 (also University of Warwick Department of Statistics Research Report 445) 

“Confidence bands for Brownian motion and applications to Monte Carlo simulation” (coauthored with J. Marin, C. P. Robert). Statistics and Computing (2007) 17: 110 (also in previous form in 2005 as “Brownian confidence bands on Monte Carlo output”, University of Warwick CRiSM Research Report 052) 

“Stochastic Integrals and their expectations” Mathematica Journal (2005) 9  
“Notes on Perfect Simulation” (coedited with F. Liang, J.S. Wang). Markov chain Monte Carlo: Innovations and Applications (2005) pp 93146 (also University of Warwick Department of Statistics Research Report 428) 


“Geometric Ergodicity and Perfect Simulation”. Electronic Communications in Probability (2004) 9:140151 (also University of Warwick Department of Statistics Research Report 427)  
“Coupling Iterated Kolmogorov Diffusions” (coauthored with C. J. Price). Electronic Journal of Probability (2004) 9:382410 (also University of Warwick Department of Statistics Research Report 416)  
“Ising models and multiresolution quadtrees” (coauthored with R. G. Wilson). Advances in Applied Probability (2003) 35:96122 (also University of Warwick Department of Statistics Research Report 402)  
“Bayesian analysis of vascular structure” (coauthored with E. Thönnes, A. Bhalerao, R. G. Wilson). LASR 2003 (2003) To appear  
“Book review: Statistics of the Galaxy Distribution, by Martínez and Saar”. Journal of the American Statistical Association (2003) 98:248  
“Simulation of cluster point processes without edge effects” (coauthored with A. Brix). Advances in Applied Probability (2002) 34:267280 (also University of Warwick Department of Statistics Research Report 382)  
“Perfect simulation for correlated Poisson random variables conditioned to be positive” (coauthored with Y. Cai). Statistics and Computing (2002) 12:229243 (also University of Warwick Department of Statistics Research Report 349)  
“Small sets and Markov transition densities” (coauthored with G. Montana). Stochastic Processes and Their Applications (2002) 99:177194 (also University of Warwick Department of Statistics Research Report 371)  
“A Bayesian approach to inferring vascular tree structure from 2D imagery” (coauthored with E. Thönnes, A. Bhalerao, R. G. Wilson); Proceedings IEEE ICIP2002 (2002) II:937939 (also University of Warwick Department of Statistics Research Report 391) 

“Symbolic Ito calculus: an ongoing story” Statistics and Computing (2001) 11:2535 (also University of Warwick Department of Statistics Research Report 327) 

“Gambling with the truth: Markov chain Monte Carlo” Challenges for the 21st Century: ICFS Mathematics and Theoretical Physics, Singapore March 2000 (2001) pp 83101 

“Inferring vascular structure from 2D and 3D imagery” (coauthored with A. Bhalerao, E. Thönnes, R. G. Wilson); Medical Image Computing and ComputerAssisted Intervention, proceedings of MICCAI 2001 (2001) 2208:820828 (also University of Warwick Department of Statistics Research Report 392) 

“Efficient Markovian couplings: examples and counterexamples” (coauthored with K. Burdzy); The Annals of Applied Probability (2000) 10:362409 (also University of Warwick Department of Statistics Research Report 331) 

“Stationary countable dense random sets” Advances in Applied Probability (2000) 32:86100 (also University of Warwick Department of Statistics Research Report 341) 

“Gambling with the Truth: Markov chain Monte Carlo” Mathematical Medley (2000) To appear 

“Perfect simulation using dominating processes on ordered state spaces, with application to locally stable point processes” (coauthored with J. Møller); Advances in Applied Probability (2000) 32:844865 (also University of Warwick Department of Statistics Research Report 347) 

“Zeros of Brownian Polynomials” (coauthored with C. J. Price); Stochastics and Stochastic Reports (2000) 70:271308 (also University of Warwick Department of Statistics Research Report 353) 

“Riemannian barycentres and geodesic convexity” (coauthored with J. M. Corcuera); Math. Proc. Camb. Phil. Soc. (1999) 127:253269 (also University of Warwick Department of Statistics Research Report 325) 

“Geometry, statistics, and shape” Geometry in Present Day Science (1999) pp 143163 (also University of Warwick Department of Statistics Research Report 319) 

“Quermassinteraction processes: conditions for stability” (coauthored with M. N. M. van Lieshout, A. J. Baddeley); Advances in Applied Probability (1999) 31:315342 (also University of Warwick Department of Statistics Research Report 293) 

“Perfect Simulation in Stochastic Geometry” (coauthored with E. Thönnes); Pattern Recognition (1999) 32:15691586 (also University of Warwick Department of Statistics Research Report 323) 

“From Stochastic Parallel Transport to Harmonic Maps” (coauthored with J. Jost, U. Mosco, M. Röckner, K. T. Sturm); hrefhttp://www.ams.org/bookstore?fn=20&arg1=amsipseries&item=AMSIP8 (1998) pp 49115 (also University of Warwick Department of Statistics Research Report 321) 

“Perfect simulation for the areainteraction point process” Probability Towards 2000 (1998) pp 218234 (also University of Warwick Department of Statistics Research Report 292) 

“Computer Algebra” Encyclopedia of Biostatistics (1998) 1:839845 (also University of Warwick Department of Statistics Research Report 301) 

“A diffusion model for Bookstein triangle shape” Advances in Applied Probability (1998) 30:317334 (also University of Warwick Department of Statistics Research Report 296) 

“On some weighted Boolean models” Advances in Theory and Applications of Random Sets (1997) pp 105120 (also University of Warwick Department of Statistics Research Report 295) 

“Perfect Simulation for Spatial Point Processes” Bulletin ISI, 51^{st} session proceedings, Istanbul (August 1997) (1997) 3:163166 (also University of Warwick Department of Statistics Research Report 308) 

“Gromov’s hyperbolicity and Picard’s little theorem for harmonic maps” (coauthored with M. Cranston, Yu. Kifer); Stochastic Analysis and Applications, Gregynog, (9^{ th}14^{ th} July 1995) (1996) pp 139164 (also University of Warwick Department of Statistics Research Report 280) 

“Coupling constructions for hypoelliptic diffusions: Two examples” (coauthored with G. Ben Arous, M. Cranston); Stochastic Analysis: Summer Research Institute July 1130, 1993 (1995) 57:193212 (also University of Warwick Department of Statistics Research Report 261) 

“The radial part of a Gammamartingale and a nonimplosion theorem” The Annals of Probability (1995) 23:479500 (also University of Warwick Department of Statistics Research Report 231) 

“Stochastic calculus, statistical asymptotics, strings and phyla” (coauthored with O. E. BarndorffNielsen, P. E. Jupp); Annales de la Faculté des Sciences de Toulouse Mathématiques (Série 6) (1994) 3:562 (also University of Warwick Department of Statistics Research Report 222) 

“Probability, convexity, and harmonic maps II: Smoothness via probabilistic gradient inequalities” Journal of Functional Analysis (1994) 126:228257 (also University of Warwick Department of Statistics Research Report 260) 

“The radial part of Brownian motion II: Its life and times on the cut locus” (coauthored with M. Cranston, P. March); Probability Theory and Related Fields (1993) 96:353368 (also University of Warwick Department of Statistics Research Report 244) 

“Doing stochastic calculus with Mathematica” Economic and Financial Modeling with Mathematica (1993) pp 214238 (also University of Warwick Department of Statistics Research Report 238) 

“Computer algebra in probability and statistics” statistica neerlandica (1993) 47:925 (also University of Warwick Department of Statistics Research Report 236) 

“On the empty cells of Poisson histograms” Journal of Applied Probability (1993) 30:561574 (also University of Warwick Department of Statistics Research Report 239) 

“Brownian motion and partial differential equations: From the heat equation to harmonic maps” Bulletin ISI, 49^{th} session proceedings, Firenze (August 1993) (1993) 3:85101 (also University of Warwick Department of Statistics Research Report 257) 

“Limiting angle of Brownian motion in certain twodimensional Cartan Hadamard manifolds” (coauthored with E. P. Hsu); Annales de la Faculté des Sciences de Toulouse Mathématiques (Série 6) (1992) 1:169186 (also University of Warwick Department of Statistics Research Report 216) 

“A remark on the proof of Itô’s formula for C^{2} functions of continuous semimartingales” Journal of Applied Probability (1992) 29:216221 (also University of Warwick Department of Statistics Research Report 202) 

“Convex geometry and nonconfluent Gammamartingales II: Wellposedness and Gammamartingale convergence” Stochastics and Stochastic Reports (1992) 38:135147 (also University of Warwick Department of Statistics Research Report 214) 

“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) 46:364374 (also University of Warwick Department of Statistics Research Report 213) 

“Correction note to ‘Martingales on manifolds and harmonic maps’” (coauthored with H. Huang); Stochastics and Stochastic Reports (1991) 37:253257 (also University of Warwick Department of Statistics Research Report 218) 

“Symbolic Itô calculus: An overview” Probabilités Numeriques (1991) pp 186192 (also University of Warwick Department of Statistics Research Report 223) 

“Convexity and the hemisphere” The Journal of the London Mathematical Society (Second Series) (1991) 43:567576 (also University of Warwick Department of Statistics Research Report 181) 

“Convex geometry and nonconfluent Gammamartingales I: Tightness and strict convexity” Stochastic Analysis, Proceedings, LMS Durham Symposium, 11th  21st July 1990 (1991) pp 163178 (also University of Warwick Department of Statistics Research Report 212) 

“Probability, convexity, and harmonic maps with small image I: Uniqueness and fine existence” Proceedings of the London Mathematical Society (Third Series) (1990) 61:371406 (also University of Warwick Department of Statistics Research Report 162) 

“A spatial Markov property for nearestneighbour Markov point processes” Journal of Applied Probability (1990) 28:767778 (also University of Warwick Department of Statistics Research Report 172) 

“The Euclidean diffusion of shape” Disorder in Physical Systems (1990) pp 203217 (also University of Warwick Department of Statistics Research Report 161) 

“Invited contribution to discussion of ‘A survey of the statistical theory of shape’ by D.G. Kendall” Statistical Science (1990) 4:111113 

“Computer algebra and stochastic calculus” Notices of the American Mathematical Society (1990) 37:12541256 (also University of Warwick Department of Statistics Research Report 203) 

“Coupled Brownian motions and partial domain monotonicity for the Neumann heat kernel” Journal of Functional Analysis (1989) 86:226236 

“Diffusion processes” Applications of probability M343 (1988) 

“Symbolic computation and the diffusion of shapes of triads” Advances in Applied Probability (1988) 20:775797 

“Busemann functions and Brownian motion” Stochastic Calculus in Applications, Symposium Proceedings, Cambridge 1986 (1988) 197:6368 

“Martingales on manifolds and harmonic maps” The Geometry of Random Motion (1988) 73:121157 

“A summary of points raised in the Discussion Sessions” (coauthored with C. T. J. Dodson, P. E. Jupp, S. L. Lauritzen); Geometrization of Statistical Theory, Proceedings of the GST Workshop, University of Lancaster, 2831 October 1987 (1987) pp 235250 

“Stochastic differential geometry: An introduction” Acta Applicandae Mathematicae. An International Journal on Applying Mathematics and Mathematical Applications (1987) 9:2960 

“The radial part of Brownian motion on a manifold: Semimartingale properties” The Annals of Probability (1987) 15:14911500 

“Computer algebra, Brownian motion, and the statistics of shape” Geometrization of Statistical Theory, Proceedings of the GST Workshop, University of Lancaster, 2831 October 1987 (1987) pp 171192 

“Discussion of read paper by Clifford, Green and Pilling” Journal of the Royal Statistical Society (Series B: Methodological) (1987) 49:286287 

“Stochastic differential geometry” Proceedings, First World Congress of the Bernoulli Society (1987) 1:515524 

“Mean values of stationary planar tessellations” (coauthored with J. Mecke); Journal of Applied Probability (1987) 24:411421 

“Scattering processes and convergence to Brownian motion” (coauthored with M. Westcott); Advances in Applied Probability (1987) 19:81105 

“A nonstandard proof of one of David Williams’ splittingtime theorems” (coauthored with N. J. Cutland); Analytic and Geometric Stochastics, Special Supplement to Advances in Applied Probability (1986) pp 3747 

“Combinatorial Laplacians and isoperimetric inequality” (coauthored with J. Dodziuk); From local times to global geometry, control, and physics (1986) 150:6874 

“Factorizations of Brownian motions and harmonic maps” (coauthored with K. D. Elworthy); From local times to global geometry, control, and physics (1986) 150:7583 

“Stochastic differential geometry, a coupling property, and harmonic maps” The Journal of the London Mathematical Society (Second Series) (1986) 33:554566 

“Nonnegative Ricci curvature and the Brownian coupling property” Stochastics and Stochastic Reports (1986) 19:111129 

“Brownian motion in 4space; is it tame?” Académie de la République Populaire Roumaine. Revue Roumaine de Mathématiques Pures et Appliquées (1985) 30:371374 

“Brownian motion on 2dimensional manifolds of negative curvature” Séminaire de Probabilités (1984) XVIII:7076 

“Brownian motion and a generalised little Picard’s theorem” Transactions of the American Mathematical Society (1983) 275:751760 

“Coupling methods and the storage equation” Journal of Applied Probability (1983) 20:436441 

“Epidemics in competition II: The general epidemic” (coauthored with I. W. Saunders); Journal of the Royal Statistical Society (Series B: Methodological) (1983) 45:238244 

“Contours and Baire category” The Bulletin of the London Mathematical Society (1982) 14:3032 

“Bias in measurement of fissiontrack length distributions” (coauthored with G. M. Laslett, A. J. W. Gleadow, I. R. Duddy); Nuclear Tracks (1982) 6:7985 

“Brownian motion, negative curvature, and harmonic maps” Stochastic Integrals, Proceedings, LMS Durham Symposium, 1980 (1981) 851:479491 

“Contours of processes with multidimensional times” Proceedings, Sixth Conference on Probability Theory, Brasov, Romania (1981) pp 317318 

“Contours of Brownian processes with severaldimensional times” Zeitschrift für Wahrscheinlichkeitstheorie und verve Gebiete (1980) 52:267276 

“Alignments in twodimensional random sets of points” (coauthored with D. G. Kendall); Advances in Applied Probability (1980) 12:380424 

“The knotting of Brownian motion in 3space” The Journal of the London Mathematical Society (Second Series) (1979) 19:378384 
If you want copies of any of the research reports then please mail or fax your requests to the departmental secretary.