Stochastic Processes

Stochastic processes involving randomness dominate in many areas of natural and man made systems. Describing their evolution quantitatively requires powerful theory from the fields of probability, statistics, and other areas of mathematics. Financial mathematics, for example, seeks to provide guidance in managing risk, and is at the core of modelling carried out by financial institutions and treasuries. The stochastic behaviour of cells, genes, and populations is the subject of Mathematical Biology.

Our world is dynamic and complex, and often not deterministic. The mathematics of stochastic processes is crucial in allowing us to understand and manage risk, randomness, and change.

Research centres

Academic Staff

A/Prof Andrea Collevecchio Stochastic processes, large deviations and applications to statistical mechanics, random graph theory, self-interacting random processes, urn models. Andrea.Collevecchio@monash.edu
Dr Kaustav Das Probability theory, stochastic analysis, mathematical finance, stochastic partial differential equations (SPDEs), fractional Brownian motion. Kaustav.Das@monash.edu
Dr Hasan Fallahgoul Theoretical and Empirical Asset pricing, financial econometrics, machine learning. Hasan.Fallahgoul@monash.edu
A/Prof Tim Garoni Mathematical physics, statistical mechanics, combinatorics (probability on graphs), Markov chain Monte Carlo methods Tim.Garoni@monash.edu
Dr Ivan Guo Financial mathematics, stochastic control, optimal transport, model calibration, robust finance, stochastic games, graph theory, machine learning. Ivan.Guo@monash.edu
Prof Kais Hamza General theory of stochastic processes, representation properties for martingales, markov jump processes, applications of stochastic processes to modelling of financial markets. Kais.Hamza@monash.edu
A/Prof Jonathan Keith Bayesian modelling and computational methods, bioinformatics, invasive species modelling and epidemiology. Jonathan.Keith@monash.edu
Prof Fima Klebaner Stochastic processes, probability; stochastic models, populations models, financial mathematics, volatility, market models, martingales, random perturbations, applied probability. Fima.Klebaner@monash.edu
Prof Gregoire Loeper Optimal transport, Financial mathematics, Non-linear PDE's, Monge-Ampere equation. Gregoire.Loeper@monash.edu
Dr Gregory Markowsky Complex analysis, graph theory, probability. Greg.Markowsky@monash.edu
Dr Daniel McInnes Stochastic control, controllable Markov chains, dynamic programming, Markov decision problems. Daniel.McInnes@monash.edu
Dr Kihun Nam Backward stochastic differential equations, optimal control of random systems such as dynamic random network, stochastic differential game, and their application to finance and biology. Kihun.Nam@monash.edu
Dr Soojin Roh Spatial statistics, multivariate statistics, data assimilation. Soojin.Roh@monash.edu
Dr Meng Shi Meng.Shi@monash.edu
A/Prof Tianhai Tian Mathematical modelling of complex biological systems, including genetic regulatory networks, cell signalling transduction pathways, and cancer therapy. Inference of complex networks from big data. Tianhai.Tian@monash.edu
Dr Yu Tian Retirement income product design and pricing, portfolio optimisation, derivatives pricing and risk management. Oscar.Tian@monash.edu

Research Fellows

Dr Minh Nguyen Probability and random processes on discrete structures. Tuanminh.Nguyen@monash.edu
Dr Zongzheng Zhou Applied probability, Statistical Mechanics, Markov chain Monte Carlo methods. Eric.Zhou@monash.edu

Adjuncts

Prof Robert Griffiths Stochastic Processes, Mathematical Population Genetics. Bob.Griffiths@monash.edu