# Stochastic Processes

## About

The Stochastic Processes Group in the Department works in the area of probability theory - a branch of mathematics providing means for modeling uncertainty. The latter is a characteristic feature of the behaviour of most complex systems - e.g. 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 knowing the laws according to which the systems evolve in time. Discovering such laws and devising methods for using them in various applications including statistics, financial engineering, risk analysis and control is the principle task of researchers working in the area of Stochastic Processes. The results of the theory turn out to be useful not only in applications to random phenomena, but also in some areas of pure and applied mathematics. Mathematically the theory of stochastic processes is a very challenging and still actively developing theory. It requires deep knowledge of different areas of mathematics, including classical calculus, functional analysis, measure and function theory, algebra and combinatorics. Computer simulations also play nowadays an ever increasing role and enable one to get insight into the behaviour of analytically yet intractable systems. Stochastic Processes graduates work in research and development departments of leading financial and insurance institutions, defence organizations, as well as in the areas of bio-informatics, signal processing and many others. Since they usually would have a concurrent training in statistics, our graduates are also highly employable in a huge variety of areas requiring specialists in statistics. Research in the Stochastic Processes Group is focused on a number of areas, ranging from more theoretical ones such as point processes approximation, the theory of stochastic networks and boundary crossing problems to applications of stochastic processes to risk modelling and financial engineering. Our group currently consists of Kostya Borovkov and Aihua Xia. They both are members of the newly established ARC Centre of Excellence for Mathematics and Statistics of Complex Systems (MASCOS). It is worth noting that a student holding an APA and undertaking a PhD under the supervision of a MASCOS member will be considered for a top-up scholarship plus an additional grant for research-related expenses.

## Academics

Professor Kostya BOROVKOV (Professor)

Professor Tim BROWN (Professor)

Dr Mark FACKRELL (Lecturer)

Dr Sophie HAUTPHENNE (Senior Lecturer)

Associate Professor Mark HOLMES (Associate Professor)

Dr Nathan ROSS (Senior Lecturer)

Professor Peter TAYLOR (Professor)

Professor Aihua XIA (Professor)

## Research Fellows

Dr Azam ASANJARANI (ARC Centre Fellow)

Dr Rhys BOWDEN (Research Fellow)

Dr Jing FU (Research Fellow)

Dr Matthieu SIMON (ARC Centre Fellow)

Dr Laleh TAFAKORI (Research Fellow)

Dr Ali TIRDAD (Research Fellow)

## Visitors

Dr Andriy OLENKO (La Trobe University)

## Postgraduate Students

Peter BRAUNSTEINS – ‘Coupling in Stochastic Modelling’

Aaron CHONG

Timothy HYNDMAN

Ashwani KUMAR

Jason LEUNG – ‘Topics in nonparametric function estimation’

Wenchao LI – ‘Efficient techniques and algorithms for sensor network localization.’

Yuqing PAN – ‘Boundary crossing problem of different types of Random processes Hitting Remote Sets.’

Nicholas READ – ‘Bush Escalation Probabilities in the Victorian Landscape’

Kate SAUNDERS – ‘Spatial and Temporal Statistical Modelling of Extreme Rainfall in Australia.’

Shrupa SHAH – ‘Understanding the contribution of space on the spread of Influenza using an Individual-based model approach’

Xuan (Kevin) VO – ‘Convergence of instantaneous markov processes’

## Masters (RT) Students

Tianshu CONG

Xin HUANG

Xuehua LAN

Cong LI

Vincent LIANG

Hangrui LIN

Meirian LOVELACE-TOZER

Anson MACDONALD

Vincent PANG

Justin SMALLWOOD

Ria SZEREDI

Yawei ZHANG