# 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 Tim BROWN** (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*

## Research Fellows

**Dr Mehdi FOUMANI** (Research Fellow)

**Dr Matthieu SIMON** (ARC Centre Fellow)

## Honorary Staff

**Professor Andrew BARBOUR**

Professorial Fellow (Associate)
**Professor Daryl DALEY**

Professorial Fellow (Associate)

## Postgraduate Students

BANOVA Tim

CHEN Zeying – ‘Exact solutions to multi-species exclusion processes’

CHONG Aaron

CONG Tianshu

ERANDI Achini

HUANG Xin

KARUNARATHNE Weerasekara

KUMAR Ashwani

LEUNG Jason – ‘Topics in nonparametric function estimation’

LIANG Vincent

LO Yin Yuan (Tiffany)

NIKNAMI Behrooz

QIAN Manling

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’

WANG Jiesen

XING Chenchen

## Masters (RT) Students

GUO Yajing

LI Xiangjun

LIN Hangrui

MEDLAND Robert

NGUYEN Duy Phat

NGUYEN Paul

PORTER Liam

QIAN Jiaxuan

SCHOLZ Adam

SHI Wenfei

SZEREDI Ria

TAN Yiting

THORBURN Luke

WEINSTOCK Edward

WU Chengrui

XING Yi

XU Qin

ZHANG Lijun

ZHENG Hanyun