# Stochastic Processes

## About

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.

## Seminar series

## Academic Staff

**Prof Kostya BOROVKOV** (Professor)

**Prof Jan DE GIER** (Professor)

Research interests: *Stochastic Processes, Integrable models, Mathematical Physics, Combinatorics*

**Dr Mark FACKRELL** (Senior Lecturer)

Research interests: *Matrix-analytic methods, Game theory, Healthcare modelling, Operations Research, Stochastic Modelling*

**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)

**Professor Mark HOLMES** (Professor)

**Dr Mario KIEBURG** (Lecturer)

Research interests: *Quantum Information Theory, Quantum Chaos, Supersymmetry & Graded Algebras, Telecommunications systems, Quantum field theory, Time Series, Orthogonal functions and polynomials, Random Matrix Theory, Harmonic Analysis and Group & Representation Theory*

**Prof Malwina LUCZAK** (Professor)

**A/Prof Nathan ROSS** (Associate Professor / Senior Lecturer)

**Prof Peter TAYLOR** (Professor)

Research interests: *Matrix-analytic methods, Markov decision processes, Complex Networks, Mechanism design, Optimisation and control, Parameter estimation, Stochastic modelling of biological/environmental systems, epidemics, telecommunications systems and emergency management systems, Queueing theory*

**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*

## Honorary Staff

**Professor Daryl DALEY**

Professorial Fellow (Associate)