Papers

• General path integrals and stable SDEs (with Sam Baguley and Leif Döring). To appear in the Journal of the European Mathematical Society.
• Many-to-few for non-local branching Markov process (with Simon Harris, Emma Horton and Ellen Powell). Electronic Journal of Probability, 29, 1-26, 2024.
• Multi-type Λ-coalescents (with Samuel Johnston and Tim Rogers). Annals of Applied Probability. Vol. 33 (6A), 4210-4237, 2023.
  
• Asymptotic moments of spatial branching processes (with Emma Horton and Isaac Gonzalez). Probability Theory and Related Fields (2022), 184 no. 3-4, 805–858. See also the Erratum for the non-critical cases in the same journal (2023), 187 no. 1-2, 505–515.
  
• Monte-Carlo Methods for the Neutron Transport Equation (with Alex M.G. Cox, Simon Harris and Minmin Wang). SIAM Journal of Uncertainty Quantification (2022), no. 2, 775–825.
• Yaglom limit for non-local critical branching Markov processes (With Emma Horton, Simon Harris and Minmin Wang). Annals of Probability (2022), Vol. 50, No. 6, 2373–2408.
• An optimal stopping problem for spectrally negative Markov additive processes (With Mine Çağlar, and Ceren Vardar-Acar). Stochastic Processes and their Applications (2022), 150, 1109-1138
• Oscillatory attraction and repulsion from a subset of the unit sphere or hyperplane for isotropic stable Lévy processes (With Mateusz Kwaśniki, Sandra Palau, and Tsogzolmaa Saizmaa). In: A Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney’s 80th Birthday. p283-313, Birkhäuser 2022.
• The Doob-McKean identity for stable Lévy processes (With Neil O'Connell). In: A Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney’s 80th Birthday. p269-282. Birkhäuser 2022.
• A Transformation for Spectrally Negative Lévy Processes and Applications (With Marie Chazal and Pierre Patie). In: A Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney’s 80th Birthday. (2022) p157-180. Birkhäuser 2022.
• A Lifetime of Excursions Through Random Walks and Lévy Processes (With Loic Chaumont). In: A Lifetime of Excursions Through Random Walks and Lévy Processes: A Volume in Honour of Ron Doney’s 80th Birthday. (2022) p1-11. Birkhäuser 2022.
• Stable Lévy processes in a cone. (with Victor M. Rivero and Weerapat Satitkanitkul). Annales de l'Instut Henri Poincaré (2021), 57, No. 4, 2066–2099.
• Double hypergeometric Lévy processes and self-similarity (With Juan Carlos Pardo and Matija Vidmar). Journal of Applied Probability (2021), 58, 254–273.
• Attraction to and repulsion from a subset of the unit sphere for isotropic stable Lévy processes (With Sandra Palau, and Tsogzolmaa Saizmaa). Stochastic Processes and their Applications (2021), 137 272-293.
• Stochastic Methods for the Neutron Transport Equation III: Generational many-to-one and k_eff. (with Alex M.G. Cox, Emma Horton and Denis Villemonais). SIAM Journal of Applied Mathematics (2021), 81(3), 982–1001.
• Stochastic Methods for the Neutron Transport Equation II: Almost sure growth. (with Emma Horton and Simon Harris). Annals of Applied Probability (2020), Vol. 30, No. 6, 2573-2612.
• Stochastic Methods for the Neutron Transport Equation I: Linear Semigroup asymptotics. (with Emma Horton and Denis Villemonais). Annals of Applied Probability (2020) Vol. 30, No. 6, 2815-2845.
• Deep factorisation of the stable process III: radial excursion theory and the point of closest reach. (with Victor M. Rivero and Weerapat Satitkanitkul). Potential Analysis (2020), 53, 1347-1375.
• Skeletal stochastic differential equations for superprocesses (With Dorottya Fekete and Joaquin Fontbona). Journal of Applied Probability. (2020) 57, 1111-1134.
• Stable processes conditioned to avoid an interval (with Leif Döring and Philip Weissmann). Stochastic Processes and their Applications (2020), Vol 130 no. 2, 471-487.
• Entrance laws at the origin of self-similar Markov processes in high dimensionsLink opens in a new window. (with Victor M. Rivero, Bati Sengul and Ting Yang). Transactions of the American Mathematical Society (2020) Vol. 373 (9), 6227-6299.
• Entrance and exit at infinity for stable jump diffusions (with Leif Döring). Annals of Probability (2020), Vol. 48, No. 3, 1220-1265.
• Skeletal stochastic differential equations for continuous-state branching process (With Dorottya Fekete and Joaquin Fontbona). Journal of Applied Probability (2019), 56, 1122-1150.
• Multi-species neutron transport equation. (with Alex M.G. Cox, Simon C. Harris and Emma Horton). Journal of Statistical Physics (2019), 176(2), 425-455.
• Conditioned real self-similar Markov processes. (with Victor M. Rivero and Weerapat Satitkanitkul). Stochastic Processes and their Applications (2019), 129, 954-977.
• Extinction properties of multi-type continuous-state branching processes (With Sandra Palau). Stochastic Processes and their Applications (2018), 128 3466–3489.
• Stable windings at the origin. (With Stavros Vakeroudis). Stochastic Processes and their Applications (2018), 128, 4309-4325.
• Unbiased "walk-on-spheres" Monte Carlo methods for the fractional Laplacian (With Ana Osojnik and Tony Shardlow). IMA J. Numer. Anal. (2018), 38 no. 3, 1550-1578.
• Stable processes, self-similarity and the unit ball. ALEA, Lat. Am. J. Probab. Math. Stat. (2018), 15, 617-690.
• Almost sure growth of supercritical multi-type continuous state branching process (With Sandra Palau and Yanxia Ren). ALEA, Lat. Am. J. Probab. Math. Stat. (2018), 15, 409-428.
• Universality in a class of fragmentation-coalescence processes. (with Steven Pagett and Tim Rogers). Annales de l'Instut Henri Poincaré. (2018), Vol. 54, No. 2, 1134-1151.
• Deep factorisation of the stable process II: potentials and applications. (with Victor M. Rivero and Bati Sengul). Annales de l'Instut Henri Poincaré. (2018), Vol. 54, No. 1, 343-362.
• A phase transition in excursions from infinity of the "fast" fragmentation-coalescence process. (with Steven Pagett, Tim Rogers and Jason Schweinsberg). Annals of Probability. (2017), Volume 45, No. 6A, 3829-3849.
• Conditioning subordinators embedded in Markov processes. (with Victor Rivero, and Bati Sengul). Stochastic Processes and their Applications. (2017), 127, 1234-1254.
• Real self-similar processes started from the origin (with Steffen Deriech and Leif Döring). Annals of Probability. (2017), Volume 45, No. 3, 1952-2003.
• The largest fragment of a homogeneous fragmentation process (With Peter Mörters and Francis Lane). Journal of Statistical Physics. (2017), 166, 1226-1246.
• Perpetual integrals for Lévy processes (with Leif Döring). Journal of Theoretical Probability (2016), Volume 29, Issue 3, pp 1192-1198.
• Optimal prediction for positive self-similar Markov processes (With Erik Baurdoux and Curdin Ott). Electronic Journal of Probability. (2016), Volume 21 paper no. 48, 1-24.
• More on hypergeometric Lévy processes (with Emma Horton). Advances in Applied Probability (2016), 48A, 153 - 158.
• Deep factorisation of the stable process. Electronic Journal of Probability. (2016), Volume 21 paper no. 23, 1-28.
• UK universities find a cash cow in the financial fall-out. The Conversation. (See also the longer version: The UK financial mathematics M.Sc.)
• An Euler-Poisson Scheme for Lévy driven SDEs (with Albert Ferreiro-Castilla and Rob Scheichl). Journal of Applied Probability. (2016), 53, 262-278.
• Branching Brownian motion in a strip: survival near criticality. (with Simon Harris and Marion Hesse). Annals of Probability. (2016), Vol. 44, No. 1, 235-275.
• Spines, skeletons and the Strong Law of Large Numbers for superdiffusions (with Maren Eckhoff and Matthias Winkel). Annals of Probability. (2015), Vol. 43, No. 5, 2594-2659.
• Potentials of stable processes (with Alex Watson). Séminaire de Probabilité XLVI. (2015), 333-344.
• The backbone decomposition for spatially dependent supercritical superprocesses (with Jose-Luis Pérez and Yanxia Ren). Séminaire de Probabilité XLVI. (2015), 33-60.
• The extended hypergeometric class of Lévy processes (with Juan Carlos Pardo and Alex Watson). Journal of Applied Probability. (2014), 51A, 391-408.
• Occupation times of refracted Lévy processes (with Juan Carlos Pardo and Jose-Luis Pérez). Journal of Theoretical Probability. (2014), 27, 1292-1315.
• New families of subordinators with explicit transition probability semigroup. (with James Burridge, Mateusz Kwasnicki, Alexey Kuznetsov.). Stochastic Processes and their Applications (2014), 124, 3480-3495.
• Survival of homogenous fragmentation processes with killing. (with Robert Knobloch). Annales de l'Instut Henri Poincaré(2014), 50, 476-491.
• The hitting time of zero for a stable process (with Alexey Kuznetsov, Juan Carlos Pardo and Alex Watson). Electronic Journal of Probability (2014), 19, 1-26.
• The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition. (with Marion Hesse). Stochastic Processes and its Applications (2014), 124, 2003-2022.
• A capped optimal stopping problem for the maximum process (with Curdin Ott). Acta Applicandae Mathematicae. (2014), 129, 147-174.
• Hitting distributions of alpha-stable processes via path censoring and self-similarity (with Juan Carlos Pardo and Alex Watson). Annals of Probability. (2014), 42, 398-430.
• Optimal dividends in the dual model under transaction costs (with Erhan Bayraktar and Kazutoshi Yamazaki). Insurance: Mathematics and Economics (2014), 54, 133-143.
• Multilevel Monte Carlo simulation for Lévy processes based on the Wiener-Hopf factorisation (with Albert Ferreiro-Castilla, Rob Scheichl and Gowri Suryanarayana). Stochastic Processes and its Applications (2014), 124, 985-1010.
• Pricing of Contingent Convertibles under Smile Conform Models. (with José Manuel Corcuera, Jan de Spiegeleer, Albert Ferreiro-Castilla, Dillip Madan and Wim Schoutens). Journal of Credit Risk (2013), 9(3), 121-140.
• On optimal dividends in the dual model (with Erhan Bayraktar and Kazutoshi Yamazaki). ASTIN Bulletin (2013), 43, 359-372.
• Spectrally negative Lévy processes perturbed by functionals of their running supremum (with Curdin Ott). Journal of Applied Probability (2012), 49, 1005-1014.
• An application of the backbone decomposition to supercritical super-Brownian motion with a barrier. (with Antonio Murillo-Salas and Jose-Luis Pérez). Journal of Applied Probability. (2012), 49, 671-684.
• Super-Brownian motion: Lp-convergence of martingales through the pathwise spine decomposition. (with Antonio Murillo-Salas). In Advances in Superprocesses and Nonlinear PDEs Series: Springer Proceedings in Mathematics & Statistics, Vol. 38 Englander, Janos; Rider, Brian C. (Eds.), 2013.
• Supercritical super-Brownian motion with a general branching mechanism and travelling waves (with Antonio Murillo-Salas, Rongli Liu and Yanxia Ren). Annales de l'Instut Henri Poincaré. (2012), 48, 661-687.
• Meromorphic Lévy processes and their fluctuation identities (with Alexey Kuznetsov, Juan Carlos Pardo). Annals of Applied Probability. (2012), 22, 1101-1135.
• An optimal stopping problem for fragmentation processes. (with Juan Carlos Pardo). Stochastic Processes and their Applications. (2012), 122, 1210-1225.
• Optimal control with absolutely continuous strategies for spectrally negative Lévy processes. (with Ronnie Loeffen and Jose-Luis Pérez). Journal of Applied Probability (2012), 49, 150-166.
• Fluctuation theory and exit systems for positive self-similar Markov processes (with Loic Chaumont, V. Rivero and Juan Carlos Pardo). Annals of Probability (2012), 40, 245-279.
• Backbone decomposition for continuous-state branching processes with immigration. (with Yanxia Ren). Statistics and Probability Letters. (2012), 82, 139-144.
• A Wiener-Hopf Monte Carlo simulation technique for Lévy process (with Alexey Kuznetsov, Juan Carlos Pardo and Kees van Schaik). Annals of Applied Probability. (2011), 21, 2171-2190.
• Travelling waves and homogeneous fragmentation. (with Julien Berestycki and Simon Harris). Annals of Applied Probability. (2011), 21, 1749-1794.
• On the excursions of reflected local time processes and stochastic fluid queues. (with Takis Konstantopoulos and Paavo Salminen). Journal of Applied Probability (2011), 48A, 79-98.
• Smoothness of scale functions for spectrally negative Lévy processes (with Terence Chan and Mladen Savov). Probability Theory and Related Fields (2011), 150, 691-708.
• A Ciesielski-Taylor type identity for positive self-similar Markov processes (with Pierre Patie). Annales de l'Instut Henri Poincaré (2011), 47/3, 917-928.
• The prolific backbone for supercritical superdiffusions. (with Julien Berestycki and Antonio Murillo). Stochastic Processes and their Applications (2011), 121/6, 1315-1331.
• The Gapeev--Kühn stochastic game driven by a spectrally positive Lévy process. (with Erik Baurdoux and Juan Carlos Pardo). Stochastic Processes and their Applications (2011), 121/6, 1266-1289.
• Old and new examples of scale functions for spectrally negative Lévy processes. (with F. Hubalek). Sixth Seminar on Stochastic Analysis, Random Fields and Applications, eds R. Dalang, M. Dozzi, F. Russo. Progress in Probability, Birkhäuser (2010), 119-146.
• Convexity and smoothness of scale functions and de Finetti's control problem. (with V. Rivero and Renming Song). Journal of Theoretical Probability (2010), 23, 547-564.
• Exact and asymptotic n-tuple laws at first and last passage. (with V. Rivero and Juan Carlos Pardo). Annals of Applied Probability (2010), Vol. 20, No. 2, 522-564.
• The Wiener-Hopf decomposition. Encyclopedia of Quantitative Finance, Wiley.
• Lévy processes. Encyclopedia of Quantitative Finance, Wiley.
• Strong law of large numbers for branching diffusions. (with Janos Englander and Simon Harris). Annales de l'Instut Henri Poincaré (2010), 46, 279-298.
• Strong law of large numbers for fragmentation processes. (with S.C. Harris and R.Knobloch). Annales de l'Instut Henri Poincaré (2010), 46, 119-134.
• Refracted Lévy processes. (with R. Loeffen). Annales de l'Instut Henri Poincaré (2010), 46, 24-44.
• A note on scale functions and the time value of ruin for Lévy insurance risk processes. (with Enrico Biffis). Insurance Mathematics and Economics (2010), 46, 85-91.
• General tax structures and the Lévy insurance risk model. (with Xiaowen Zhou). Journal of Applied Probability (2009), 46, 1146-1156.
• The Shepp-Shiryaev stochastic game driven by a spectrally negative Lévy process. (with Erik Baurdoux). Theory of Probability and Its Applications (Teoriya Veroyatnostei i ee Primeneniya) (2009), 53, 481-499.
• Some explicit identities associated with positive self-similar Markov processes. (with Loic Chaumont and Juan Carlos Pardo). Stochastic Processes and Their Applications (2009), 119/3, 980-1000.
• Branching processes in random environment die slowly. (with V.Vatutin). Discrete Mathematics & Theoretical Computer Science Proceedings Fifth Colloquium on Mathematics and Computer Science (2008), 375-396.
• Analysis of stochastic fluid queues driven by local time processes. (with Takis Konstantopoulos, Paavo Salminen and Marina Sirvio (née Kozlova)). Advances of Applied Probability (2008), vol. 40 (4), 1072-1103.
• Continuous state branching processes and self-similarity. (with Juan Carlos Pardo). Journal of Applied Probability (2008), 45 (4), 1140-1160.
• Special, conjugate and complete scale functions for spectrally negative Lévy processes. (with V. Rivero). Electronic Journal of Probability (2008), Paper no 57, 1672-1701.
• On the parabolic generator of a general one-dimensional Lévy process. (with Nathalie Eisenbaum). Electronic Communications in Probability (2008), Paper no. 20, 198-209.
• Fluctuations of spectrally negative Markov Additive Processes. (with Z. Palmowski). Séminaire de Probabilité XLI. 121-135.
• The McKean stochastic game driven by a spectrally negative Lévy process. (with Erik Baurdoux). Electronic Journal of Probability. (2008), Paper no. 8, 173-197.
• Callable puts as composite exotic options. (with C. Kuhn). Mathematical Finance (2007), 17, 487-502.
• A note on the change of variable formula with local time-space for bounded variation Lévy processes. (With B. Surya). Séminaire de Probabilité XL. 97-105.
• Distributional study of De Finetti's dividend problem for a general Lévy insurance risk process. (with Z. Palmowski). Journal of Applied Probability. (2007), 44, 428-443.
• Pricing Isreali options: a pathwise approach. (with C. Kuhn and K. van Schaik). Stochastics (2007), 79, 117-137.
• Principles of smooth and continuous fit in the determination of endogenous bankruptcy levels. (with B. Surya). Finance and Stochastics (2007), 11, 131-152.
• Quasi-stationary distributions for Lévy process. (with Z. Palmowski). Bernoulli (2006), 12, 571-581.
• On extreme ruinous behaviour of Lévy insurance risk processes. (with C. Kluppelberg). Journal of Applied Probability (2006), 43, 594-598.
• Overshoots and Undershoots of Lévy process (with Ron Doney). Annals of Applied Probability (2006), 16, 91-106.
• First passage of reflected strictly stable processes. ALEA (2006), 2, 119-123.
• Further probabilistic analysis of the Fisher-Kolmogorov-Petrovskii-Piscounov equation: one sided travelling waves. (with John Harris and S. C. Harris). Annales de l'Instut Henri Poincaré (2006), 42, 125-145.
• On the Novikov-Shiryaev optimal stopping problem in continuous time. (with B. Surya). Electronic Communications in Probability (2005), 10, 146-154.
• Some remarks on first passage of Lévy process, the American put and pasting principles. (with Larbi Alili). Annals of Applied Probability (2005), 15, 2062--2080.
• The smoothing transform: the boundary case. (with J.D. Biggins). Electronic Journal of Probability (2005), 10, 609-631.
• Lévy processes in finance distinguished by their coarse and fine path properties. (with Ronnie Loeffen). In Exotic option pricing and advanced Lévy models. Eds. A. Kyprianou, W. Schoutens and P. Wilmott. Wiley, 2005.
• Finite expiry Russian options. (with Kees van Schaik and Hans Duistermaat). Stochastic Processes and their Applications. (2005), Vol 115/4, 609-638.
• Asymptotic radial speed of the support of supercritical branching Brownian motion and super-Brownian motion in R^d. Markov Processes and Related Fields. (2005), 11, 145-156.
• Further calculations for Israeli options. (with Erik Baurdoux). Stochastics. (2004), 76, 549-569.
• A martingale review of some fluctuation theory for spectrally negative Lévy processes. (with Z. Palmowski). Séminaire de Probabilité XXXVIII, 16-29.
• Measure change in multitype branching. (with J.D. Biggins). Advances in Applied Probability (2004), 36(2) 544-581.
• Ruin probabilties and overshoots for general Lévy insurance risk process. (with C. Kluppelberg and Ross Maller). Annals of Applied Probability. (2004), 14(4), 1766-1801.
• Travelling wave solutions to the K-P-P equation: alternitives to Simon Harris' probabilistic analysis. Annales de l'Instut Henri Poincaré. (2004), 40(1), 53-72.
• Exit problems for spectrally negative Lévy processes adn applications to (Canadized) Russian options. (with F.Avram and Martijn Pistorius). Annals of Applied Probability (2004), 14(1), 215-238.
• Local extinction versus local exponential growth for spatial branching processes. (with Janos Englander) Annals of Probability (2004), 32, 78-99.
• Some calculations for Israeli options. Finance and Stochastics. (2004), 8, 73 - 86.
• Law of the iterated logarithm for oscillating random walks conditioned to stay non-negative. (with B. Hambly and G.Kersting) Stochastic Processes and their Applications (2003), Vol 108/2 pp 327-343.
• Perpetual options and Canadization through fluctuation theory. (with Martijn Pistorius). Annals of Applied Probability (2003), 13(3), 1077-1098.
• A note on the alpha-quantile option. (with Laura Ballotta). Applied Mathematical Finance (2001), 8, 137--144.
• Martingale convergence and the functional equation in the multi-type branching random walk. (with A. Rahimzadeh Sani). Bernoulli. (2001), 7(4), 593--604.
• Martingale Convergence and the Stopped Branching Random Walk. Probability Theory and Related Fields (2000), 116, 405--419.
• A note on branching Lévy processes. Stochastic Processes and their Applications (1999), 82, 1-14.
• Slow variation and uniqueness of solutions to the functional equation in the branching random walk. Journal of Applied Probability (1998), 35, 795-802.
• Seneta-Heyde norming in the branching random walk. (with J.D. Biggins). Annals of Probabability (1997), 25, 337-360.
• Branching Random Walk: Seneta-Heyde norming. (with J.D. Biggins). In Trees (B.Chauvin, S. Cohen, and A. Rouault, eds) Birkhaser, Basel, 1995.

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