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.
In addition to the excellence of research, the group attracts many PhD students each year and runs a successful MSc programme in Mathematical Finance jointly with Manchester Business School and a successful MSc programme in Actuarial Science.
One output of the group is the publication of a Research Report series. An archive of the reports (dating back to 2005) is available.