Probability and Stochastic Analysis

The research in Probability and Stochastic Analysis at Manchester covers a wide range of topics. The group is internationally recognised for its numerous and significant contributions to the theory of random walks and Levy processes; Brownian motion and diffusion processes; Markov, branching and point processes; Dirichlet forms; stochastic analysis; stochastic calculus; stochastic differential equations; stochastic partial differential equations; optimal stopping and optimal stochastic control. The group has successful research collaborations with many groups in the UK and worldwide, including Aarhus, Angers, Beijing, Bielefield, Canberra, Copenhagen, Debrecen, Heidelberg, Groningen, Hong Kong, Kaiserslautern, Kiev, Kyoto, Lausanne, Moscow, Osaka, Oslo, Paris, Seattle, Stockholm, Tampere, Tokyo, Uppsala and Utrecht.

Lead Researchers:

Dr Neil Walton

Neil’s research interests lie in the areas of applied probability, operations research, optimization/control and game theory. He focuses on resource allocation in random and adversarial environments. For instance, assigning traffic signals under random demand; congestion in internet; and the prediction, assignment and purchase of adverts on search engines. Further, he has interests in financial mathematics as a senior lecturer in Actuarial Sciences and as lecturer in control theory and portfolio optimization in the Financial Mathematics MSc.

 

Dr Ronnie Loeffen

Ronnie is a Lecturer in Financial Actuarial Science at the University. His research interests include Lévy processes, Stochastic control problems, insurance mathematics and financial mathematics. Some of his past work includes Refracted Lévy processesAn optimal dividends problem with transaction costs for spectrally negative Lévy processes and Smoothness of continuous state branching with immigration semigroups

 

 

Dr Alexander Watson

Alex is a Lecturer in Actuarial Science at the University. His research interests include Lévy processes and applications, Insurance risk and ruin, (Growth-)fragmentation processes and (Continuous state) branching processes. Some of his past work includes Probabilistic aspects of critical growth-fragmentation equationsThe extended hypergeometric class of Lévy processes and Potentials of stable processes.

 

 

Professor Goran Peskir

Goran is a Professor of Probability at the University. His research interests include Brownian motion, stochastic calculus, Markov processes, optimal stopping, optimal stochastic control, free boundary problems, financial mathematics and economics. Some of his past work includes Constrained dynamic optimality and binomial terminal wealthStochastic differential equations for sticky Brownian motion and Quickest detection problems for Bessel processes.

Dr Robert Gaunt

Robert is a Dame Kathleen Ollerenshaw Fellow at the School of Mathematics. His research interests include distributional approximations and Stein's method, probability distributions, networks, special functions.  In his Network analysis work he looks at Poisson and compound Poisson approximation of the distribution of subgraph counts in stochastic block models and random graphs with multiple edges, along with network comparison and development of new measures to assess network similarity.