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 CollevecchioStochastic processes, large deviations and applications to statistical mechanics, random graph theory, self-interacting random processes, urn models.Andrea.Collevecchio@monash.edu
Dr Kaustav DasProbability theory, stochastic analysis, mathematical finance, stochastic partial differential equations (SPDEs), fractional Brownian motion.Kaustav.Das@monash.edu
Dr Hasan FallahgoulTheoretical and Empirical Asset pricing, financial econometrics, machine learning.Hasan.Fallahgoul@monash.edu
A/Prof Tim GaroniMathematical physics, statistical mechanics, combinatorics (probability on graphs), Markov chain Monte Carlo methodsTim.Garoni@monash.edu
Dr Ivan GuoFinancial mathematics, stochastic control, optimal transport, model calibration, robust finance, stochastic games, graph theory, machine learning.Ivan.Guo@monash.edu
Prof Kais HamzaGeneral 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 KeithBayesian modelling and computational methods, bioinformatics, invasive species modelling and epidemiology.Jonathan.Keith@monash.edu
Prof Fima KlebanerStochastic processes, probability; stochastic models, populations models, financial mathematics, volatility, market models, martingales, random perturbations, applied probability.Fima.Klebaner@monash.edu
Prof Gregoire LoeperOptimal transport, Financial mathematics, Non-linear PDE's, Monge-Ampere equation.Gregoire.Loeper@monash.edu
Dr Gregory MarkowskyComplex analysis, graph theory, probability.Greg.Markowsky@monash.edu
Dr Daniel McInnesStochastic control, controllable Markov chains, dynamic programming, Markov decision problems.Daniel.McInnes@monash.edu
Dr Kihun NamBackward 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 RohSpatial statistics, multivariate statistics, data assimilation.Soojin.Roh@monash.edu
A/Prof Tianhai TianMathematical 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 TianRetirement income product design and pricing, portfolio optimisation, derivatives pricing and risk management.Oscar.Tian@monash.edu

Research Fellows

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

Adjuncts

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