Papers and Publications

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Recent Publications

Levy processes - from probability theory to finance and quantum groups, Notices of the American Math Soc. 51, 1336-47 (2004) .pdf

Levy-type stochastic integrals with regularly varying tails, Stochastic Analysis and its Applications, 23, 1-18 (2005) .pdf

Martingale-valued measures, Ornstein-Uhlenbeck processes with jumps and operator self-decomposability in Hilbert space, Seminaire de Probabilites 39 171-97 (2005) .pdf   Author's post-publication comment.pdf

Brownian motion and Levy processes on locally compact groups, Methods of Functional Analysis and Topology, 12 101-112 (2006).pdf

Covariant Mehler semigroups in Hilbert space, Markov Processes and Related Fields 13, 159-69 (2007).pdf   Author's post-publication comment.pdf

On the infinitesimal generators of Ornstein-Uhlenbeck processes with jumps in Hilbert Space, Potential Analysis 26 79-100 (2007).pdf

Levy processes and stochastic integrals in Banach spaces, Probability and Mathematical Statistics 27 75-88 (2007) .pdf   Author's post-publication comment.pdf

A Levy-Cielsielski Expansion for Quantum Brownian Motion and the Construction of Quantum Brownian Bridges, Journal of Applied Analysis, 13, 275-90 (2007) .pdf

Probability Measures on Compact Groups which have Square-Integrable Densities , Bulletin of the London Math Soc., 40, 1038-44 (2008) .pdf   Corrigendum 42 948 (2010) .pdf

Universal Malliavin calculus in Fock and Levy-Ito spaces, Communications on Stochastic Analysis 3, 119-41 (2009) .pdf

Some $L^{2}$ Properties of Semigroups of Measures on Lie Groups, Semigroup Forum 79, 217-28 (2009) .pdf   Author's post-publication comment.pdf

Asymptotic Stability of Stochastic Differential Equations Driven by Levy Noise (co-author: Michailina Siakalli )), Journal of Applied Probability 46, 1116-29 (2009) .pdf

Extending Stochastic Resonance for Neuron Models to General Levy Noise, IEEE Transactions on Neural Networks 20, 1993-6 (2009) .pdf

Stochastic Stabilization of Dynamical Systems using Levy Noise (co-author: Michailina Siakalli ), Stochastics and Dynamics 10, 509-27 (2010).pdf

Robin Hudson's Pathless Path to Quantum Stochastic Calculus, Communications on Stochastic Analysis 4, 481-91 (2010) .pdf   Author's post-publication comment.pdf

Cylindrical Levy processes in Banach spaces (co-author: Markus Riedle ) Proc. London Math. Soc. 101, 697-726 (2010) .pdf

Probability on Compact Lie Groups, in International Encyclopedia of Statistical Sciences 1121-23 (2011).pdf   Author's post-publication comment.pdf

Pseudo Differential Operators and Markov Semigroups on Compact Lie Groups , Journal of Mathematical Analysis and Applications 384, 331-48 (2011) .pdf   Author's post-publication comment.pdf

Infinitely Divisible Central Probability Measures on Compact Lie Groups - Regularity, Semigroups and Transition Kernels , Annals of Probability 39, 2474-96 (2011) .pdf   Author's post-publication comment.pdf

Aspects of Recurrence and Transience for Levy Processes in Transformation Groups and Non-Compact Riemannian Symmetric Pairs, Journal of The Australian Math. Soc 94, 304-20 (2013) .pdf Authors' post-publication comment.pdf

Smoothness of Densities on Compact Lie Groups , Rendiconti del Seminario Matematico Torino 19 No.2 197-209 (2013) .pdf

Second quantisation for skew convolution products of measures in Banach spaces, (co-author: Jan van Neerven ), Electronic Journal of Probability 19, paper 11 (17 pages) (2014) .pdf   Author's post-publication comment.pdf

Martingale transform and Levy Processes on Lie Groups , (co-author: Rodrigo Banuelos ), Indiana University Math. Journal 63, 1109-38 (2014) .pdf

Probabilistic Approach to Fractional Integrals and the Hardy-Littlewood-Sobolev Inequality , (co-author: Rodrigo Banuelos ), in ``Analytic Methods in Interdisciplinary Applications'', Springer Proc. Math. Stat. Vol. 116, pp. 17-40 (2014) .pdf   Authors' post-publication comment.pdf

Second quantisation for skew convolution products of infinitely divisible measures, (co-author: Jan van Neerven ), Infinite Dimensional Analysis and Quantum Probability 18, 155003 (12 pages) (2015) .pdf

A generalised Gangolli-Levy-Khintchine formula for infinitely divisible measures and Levy processes on semi-simple Lie groups and symmetric spaces , (co-author: Tony Dooley ), Annales Institut Henri Poincare (Prob.Stat.) 51, 599-619 (2015) .pdf  Authors' post-publication comment.pdf

Infinite dimensional Ornstein-Uhlenbeck processes driven by Levy processes, Probability Surveys 12, 33-54 (2015) .pdf

The Kalman-Bucy Filter for Integrable Levy Processes with Infinite Second Moment, (co-author: Stefan Blackwood ), Journal of Applied Probability 52, 636-48 (2015) .pdf

Stationary random fields on the unitary dual of a compact group, Seminaire de Probabilites XLVIII, Lecture Notes in Math Vol. 2168, 469-80 (2016) .pdf

Convolution semigroups of probability measures on Gelfand pairs, revisited, Communications on Stochastic Analysis 10, 473-90 (2016) .pdf  Authors' post-publication comment.pdf

Probabilistic trace and Poisson summation formulae on locally compact abelian groups, Forum Math. 29, 501-17 (2017) .pdf   Corrigendum, Forum Math.29, 1499-1500 (2017) .pdf

Transition Densities and Traces for Invariant Feller Processes on Compact Symmetric Spaces, (co-author: Trang Le Ngan ) .pdf Potential Analysis 49 , 479-501 (2018) ;Authors' comment.pdf

On the Spectrum of Self-Adjoint Levy Generators, .pdf , Communications on Stochastic Analysis 13 , Number 1, Article 4 (2019)


The Positive Maximum Principle on Lie Groups, (co-author: Trang Le Ngan ) .pdf , to appear in J.London Math.Soc.

The Positive Maximum Principle on Symmetric Spaces, (co-author: Trang Le Ngan ) .pdf

L^2 Properties of Levy Generators on Compact Riemannian Manifolds, (co-author: Rosemary Shewell Brockway ) .pdf , to appear in J.Theor.Prob.

Markov Processes with Jumps on Manifolds and Lie Groups, (co-author: Ming Liao ) .pdf

School of Mathematics and Statistics

Last updated 16th December 2019