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.
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.