Probability is a beautiful and ubiquitous field of modern mathematics that can be loosely described as the mathematics of uncertainty. It has applications in all areas of pure and applied science, and provides the theoretical basis for statistics. Four of the last twelve Fields Medallists have been recognised for their work in probability.
Stochastic processes involves the study of systems that evolve randomly in time. The latter is a characteristic feature of the behaviour of most complex systems, for example, living organisms, large populations of individuals of some kind (molecules, cells, stars or even students), financial markets, systems of seismic faults etc. Being able to understand and predict the future behaviour of such systems is of critical importance, and this requires understanding the laws according to which the systems evolve in time. Discovering such laws and devising methods for using them in various applications in physics, biology, statistics, financial engineering, risk analysis and control is the principle task of researchers working in the area of stochastic processes. Computer simulations also play an important role in the field, and enable one to get insight into the behaviour of analytically intractable systems.
Research in our group covers a diverse range of theoretical and applied probability and stochastic processes, including: stochastic approximation, the theory of queues and stochastic networks, random walks, random graphs and combinatorial structures, reinforcement processes, interacting particle systems, stochastic dynamical systems, boundary crossing problems, and applications in epidemiology, healthcare, traffic management, risk modelling, financial engineering.
Students interested in pursuing a career in various fields such as mathematics, statistics, physics, biology, finance, economics etc. will benefit greatly by studying probability at a deep level. Stochastic Processes graduates work in research and development departments of leading financial and insurance institutions, defence organisations, as well as in the areas of bioinformatics, signal processing, technology and many others.
Prof Kostya BOROVKOV (Professor)
Prof Jan DE GIER (Head of School)
Research interests: Stochastic Processes, Integrable models, Mathematical Physics, Combinatorics
Dr Mark FACKRELL (Lecturer)
Research interests: Stochastic Modelling, Operations Research, Healthcare modelling, Game theory, Matrix-analytic methods
Dr Xi GENG (Lecturer)
Research interests: Stochastic Differential Equations, Rough Path Theory, Gaussian Analysis and the Malliavin Calculus, Stochastic Analysis on Manifolds
Dr Sophie HAUTPHENNE (Senior Lecturer)
A/Prof Mark HOLMES (Associate Professor)
Dr Mario KIEBURG (Lecturer)
Research interests: Harmonic Analysis and Group & Representation Theory, Random Matrix Theory, Orthogonal functions and polynomials, Time Series, Quantum field theory, Telecommunications systems, Supersymmetry & Graded Algebras, Quantum Chaos, Quantum Information Theory
Prof Malwina LUCZAK (Professor)
Dr Nathan ROSS (Senior Lecturer)
Prof Peter TAYLOR (Professor)
Research interests: Stochastic Processes, Markov processes, Queueing Networks, Telecommunications systems, Modelling of biological systems, Parameter estimation, Stochastic Petri nets
Dr Michael WHEELER (Senior Lecturer)
Research interests: Algebraic Combinatorics, Exactly solvable lattice models , Stochastic Processes, Integrable probability, Symmetric function theory
Prof Aihua XIA (Professor)
Research interests: Limit Theory in Stochastic Processes, Poisson and compound Poisson approximations, Markov processes, Queueing Networks, Point Processes
Prof Takis KONSTANTOPOULOS (The University of Liverpool)
LO Yin Yuan (Tiffany)
SHAH Shrupa – ‘Understanding the contribution of space on the spread of Influenza using an Individual-based model approach’
VO Xuan (Kevin) – ‘Convergence of instantaneous markov processes’
Masters (RT) Students
NGUYEN Duy Phat