Papers and publications


Markov Processes with Jumps on Manifolds and Lie Groups (PDF, 340KB)
(co-author: Ming Liao) Geometry and Invariance in Stochastic Dynamics, pp. 25–46.


L^2 Properties of Levy Generators on Compact Riemannian Manifolds (PDF, 318KB)
Rosemary Shewell Brockway) Journal of Theoretical Probability 34, pp. 1029-1042.


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.


On the Spectrum of Self-Adjoint Levy Generators (PDF, 197KB)
Communications on Stochastic Analysis 13, no. 1, Article 4.


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)


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..


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)


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.


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)


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.


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)


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.


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.


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)


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.


Brownian motion and Levy processes on locally compact groups (PDF, 197KB)
Methods of Functional Analysis and Topology, 12, pp. 101-112.


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)


Levy processes - from probability theory to finance and quantum groups (PDF, 169KB)
Notices of the American Mathematical Society, 51, pp. 1336-1347.