Papers and publications
2022
Markov Processes with Jumps on Manifolds and Lie Groups (PDF, 340KB)
(co-author: Ming Liao) Geometry and Invariance in Stochastic Dynamics, pp. 25–46.
2021
L^2 Properties of Levy Generators on Compact Riemannian Manifolds (PDF, 318KB)
(co-author: Rosemary Shewell Brockway) Journal of Theoretical Probability 34, pp. 1029-1042.
2020
The Positive Maximum Principle on Lie Groups (PDF, 338KB)
(co-author: Trang Le Ngan) Journal of the London Mathematical Society 101, pp. 136-155.
The Positive Maximum Principle on Symmetric Spaces (PDF, 305KB)
(co-author: Trang Le Ngan) Positivity 24, pp. 1519-1533.
2019
On the Spectrum of Self-Adjoint Levy Generators (PDF, 197KB)
Communications on Stochastic Analysis 13, no. 1, Article 4.
2018
Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces (PDF, 353KB)
(co-author: Trang Le Ngan) Potential Analysis 49, pp. 479-501.
Authors' comment (PDF, 96KB)
2017
Probabilistic trace and Poisson summation formulae on locally compact abelian groups (PDF, 392KB)
Forum of Mathematics 29, 501-517.
Corrigendum (PDF, 160KB)
Forum of Mathematics 29, pp. 1499-1500..
2016
Stationary random fields on the unitary dual of a compact group (PDF, 258KB)
Seminaire de Probabilites XLVIII, Lecture Notes in Math, vol. 2168, pp. 469-80
Convolution semigroups of probability measures on Gelfand pairs, revisited (PDF, 330KB)
Communications on Stochastic Analysis 10, pp. 473-490.
Authors' post-publication comment (PDF, 52KB)
2015
Second quantisation for skew convolution products of infinitely divisible measures (PDF, 371KB)
(co-author: Jan van Neerven), Infinite Dimensional Analysis and Quantum Probability 18, 155003. (12 pages)
A generalised Gangolli-Levy-Khintchine formula for infinitely divisible measures and Levy processes on semi-simple Lie groups and symmetric spaces (PDF, 374KB)
(co-author: Tony Dooley), Annales Institut Henri Poincare (Probability and Statistics) 51, pp. 599-619.
Authors' post-publication comment (PDF, 118KB)
Infinite dimensional Ornstein-Uhlenbeck processes driven by Levy processes (PDF, 283KB)
Probability Surveys 12, pp. 33-54.
The Kalman-Bucy Filter for Integrable Levy Processes with Infinite Second Moment (PDF, 425KB)
(co-author: Stefan Blackwood), Journal of Applied Probability 52, pp. 636-648.
2014
Second quantisation for skew convolution products of measures in Banach spaces (PDF, 381KB)
(co-author: Jan van Neerven), Electronic Journal of Probability 19, paper 11 (17 pages)
Author's post-publication comment (PDF, 57KB)
Martingale transform and Levy Processes on Lie Groups (PDF, 470KB)
(co-author: Rodrigo Banuelos), Indiana University Mathematics Journal 63, pp. 1109-1138.
Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality (PDF, 335KB)
(co-author: Rodrigo Banuelos), in "Analytic Methods in Interdisciplinary Applications'', Springer Proceedings in Mathematics and Statistics, vol. 116, pp. 17-40.
Authors' post-publication comment (PDF, 97KB)
2013
Aspects of Recurrence and Transience for Levy Processes in Transformation Groups and Non-Compact Riemannian Symmetric Pairs (PDF, 141KB)
Journal of The Australian Mathematics Society 94, pp. 304-320.
Authors' post-publication comment (PDF, 50KB)
Smoothness of Densities on Compact Lie Groups (PDF, 111KB)
Rendiconti del Seminario Matematico Torino 19, no. 2, pp. 197-209.
2011
Probability on Compact Lie Groups (PDF, 117KB)
International Encyclopedia of Statistical Sciences, 2011, pp. 1121-1123.
Author's post-publication comment (PDF, 38KB)
Pseudo Differential Operators and Markov Semigroups on Compact Lie Groups (PDF, 359KB)
Journal of Mathematical Analysis and Applications, 384, pp. 331-348.
Author's post-publication comment (PDF, 73KB)
Infinitely Divisible Central Probability Measures on Compact Lie Groups - Regularity, Semigroups and Transition Kernels (PDF, 241KB)
Annals of Probability 39, pp. 2474-2496.
Author's post-publication comment (PDF, 41KB)
2010
Stochastic Stabilization of Dynamical Systems using Levy Noise (PDF, 203KB)
(co-author: Michailina Siakalli), Stochastics and Dynamics 10, pp. 509-27.
Robin Hudson's Pathless Path to Quantum Stochastic Calculus (PDF, 170KB)
Communications on Stochastic Analysis 4, pp. 481-91.
Author's post-publication comment (PDF, 15KB)
Cylindrical Levy processes in Banach spaces (PDF, 306KB)
(co-author: Markus Riedle) Proceedings of the London Mathematical Society, 101, pp. 697-726.
2009
Universal Malliavin calculus in Fock and Levy-Ito spaces (PDF, 275KB)
Communications on Stochastic Analysis 3, pp. 119-141.
Some Lévy Properties of Semigroups of Measures on Lie Groups (PDF, 195KB)
Semigroup Forum 79, 217-228.
Author's post-publication comment (PDF, 84KB)
Asymptotic Stability of Stochastic Differential Equations Driven by Levy Noise (PDF, 185KB)
(co-author: Michailina Siakalli), Journal of Applied Probability 46, 1116-1129.
Extending Stochastic Resonance for Neuron Models to General Lévy Noise (PDF, 120KB)
IEEE Transactions on Neural Networks 20, 1993-1996.
2008
Probability Measures on Compact Groups which have Square-Integrable Densities (PDF, 160KB)
Bulletin of the London Math Society, 40, pp. 1038-1044.
Corrigendum (PDF, 133KB), 42, p. 948 (2010)
2007
Covariant Mehler semigroups in Hilbert space (PDF, 156KB)
Markov Processes and Related Fields, 13, pp. 159-169.
Author's post-publication comment (PDF, 26KB)
On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert Space (PDF, 247KB)
Potential Analysis, 26, pp. 79-100.
Levy processes and stochastic integrals in Banach spaces (PDF, 174KB)
Probability and Mathematical Statistics, 27, pp.75-88.
Author's post-publication comment (PDF, 65KB)
A Levy-Cielsielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges (PDF, 188KB)
Journal of Applied Analysis, 13, pp. 275-90.
2006
Brownian motion and Levy processes on locally compact groups (PDF, 197KB)
Methods of Functional Analysis and Topology, 12, pp. 101-112.
2005
Levy-type stochastic integrals with regularly varying tails (PDF, 206KB)
Stochastic Analysis and its Applications, 23, pp. 1-18.
Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space (PDF, 254KB)
Seminaire de Probabilites, 39, pp. 171-97.
Author's post-publication comment (PDF, 47KB)
2004
Levy processes - from probability theory to finance and quantum groups (PDF, 169KB)
Notices of the American Mathematical Society, 51, pp. 1336-1347.