The group enjoys worldwide collaborations with leading research centres and close ties with industry. The main research themes developed within the group include:
- Theoretical and numerical stochastic analysis: analysis of Markovian models; construction of Markovian projections of non-Markovian models;ordinary and partial stochastic differential equations; nonlinear filtering and stochastic control; development of efficient solvers for SDEs
- Development of new probabilistic methods and approaches to stability, performance and rare events analysis of complex stochastic processes. Limiting behaviour of stochastic models for queueing systems and networks, and of objects from stochastic geometry and percolation theory; probabilistic analysis of algorithms and communication protocols; rare events analysis for stochastic models with heavy-tailed inputs; applications to (tele)communication and power systems, transport and risk.
- Statistical methods and applications: inference for hierarchical multivariate random effects models, hidden Markov models, non-linear hierarchical models, nonparametric wavelet and spline models for smoothing, sparse models; applications to population mortality data, evaluation of evidence in forensic science and the law, agriculture, functional genomics, and model approximation in engineering sciences; Bayesian methods for fitting and testing stochastic dynamical models to partial observations in epidemiology, ecology, and medical, engineering and environmental sciences.
- Applications in financial and actuarial mathematics including theory of arbitrage, pricing of derivative products, optimisation of investment strategy, and modelling stochastic volatility in markets. Quantitative risk management, genetics and insurance, stochastic models for mortality and morbidity,stochastic economic scenario generators, modelling credit and liquidity risk in financial markets and banking, modelling policyholder behaviour in insurance.