# 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: *Combinatorics, Integrable models, Mathematical Physics, Stochastic Processes*

**Dr Mark FACKRELL** (Senior Lecturer)

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

**Prof Aihua XIA** (Professor)

Research interests: *Limit Theory in Stochastic Processes, Markov processes, Point Processes, Poisson and compound Poisson approximations, Queueing Networks*

**Prof Peter TAYLOR** (Professor)

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

**A/Prof Sophie HAUTPHENNE** (Associate Professor)

**Dr Mario KIEBURG** (Senior Lecturer)

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

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

**Professor Mark HOLMES** (Professor)

**Dr Xi GENG** (Lecturer)

Research interests: *Gaussian Analysis and the Malliavin Calculus, Rough Path Theory, Stochastic Analysis on Manifolds, Stochastic Differential Equations*

## Research Fellows

**A/Prof Michael WHEELER** (ARC Future Fellow)

Research interests: *Algebraic Combinatorics, Combinatorics, Exactly solvable lattice models , Integrable probability, Stochastic Processes, Symmetric function theory*