Mathematical Sciences


Stochastic analysis

Stochastic analysis is one of the most active and important basic research areas in mathematics. Rooted in probability and measure theory, beginning with the fundamental work of Wiener, Kolmogorov, Levy and Ito, stochastic analysis has intrinsic and deep connections and many applications in analysis and partial differential equations, geometry, dynamical systems, physics, geophysics, engineering, biology etc. in which many problems are modelled by stochastic differential equations or stochastic partial differential equations. Stochastic analysis has become the basic mathematics for mathematical finance thanks to the pioneering idea of Black, Scholes and Merton. It has been a main research area in probability theory in recent years and the trend is still increasing.

In our group, the research topics include: Stochastic analysis, in particular interactions with analysis; Stochastic methods in (nonlinear) partial differential equations and mathematical physics; Stochastic dynamical systems; Stochastic differential equations; Stochastic partial differential equations; Infinite-dimensional analysis; Stochastic analysis on geometric spaces; Markov processes and Dirichlet forms; Quantum stochastic analysis; Rough path; Schramm Loewner evolution; and Mathematics of finance.

Academic staff within this group are:

  • Dr Wael Bahsoun: Ergodic Theory and Dynamical Systems, Random Dynamical Systems, Random Dynamics in Finance and Economics.
  • Dr Chunrong Feng: Stochastic analysis, random dynamical systems, local time, rough path and financial mathematics.
  • Dr József Lörinczi: Spectral properties of non-local operators and related random processes with jump discontinuities, Feynman-Kac-type formulae, Gibbs measures on path space, applications in rigorous quantum theory.
  • Professor Huaizhong Zhao: Stochastic analysis, especially stochastic partial differential equations, stochastic dynamical systems, stochastic flows, rough path, local times, interaction with analysis, mathematics of finance.

Research students:

  • Samuel Durugo: Spectral properties of non-local operators through functional integration methods.
  • Xue Li: A Study of Random Processes Generated by Non-local Operators and Related Spectral Properties.
  • Ye Luo: Stochastic partial differential equations.