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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.
We have established the Loughborough - Shandong joint PhD programme in stochastic analysis since 2003.
The group holds weekly seminars.
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Academic staff
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| Dr Wael Bahsoun |
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Ergodic theory, dynamics of financial markets, portfolio theory, random dynamical systems. |
| Dr Chunrong Feng |
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Stochastic analysis, random dynamical systems, local time, rough path and financial mathematics. |
| Dr Mohammud Foondun |
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Probability and Stochastic Analysis mainly stochastic differential equations and stochastic partial differential equations. |
| Professor Robin Hudson |
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Quantum stochastic calculus. Current interests include rigorous analytic theory of double product integrals in this calculus, which have algebraic applications in quantising Lie bialgebras, and classical stochastic processes constructed as Casimir operators from a Capelli determinant of quantum processes. |
| Dr József Lörinczi |
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Applications of stochastic analysis to quantum theory; Feynman-Kac-type formulae, functional integration, Gibbs measures on path space, related operator semigroups and heat kernels; developing new tools by combining rough paths analysis with cluster expansion. |
| Professor Huaizhong Zhao |
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Stochastic analysis, especially stochastic partial differential equations, stochastic dynamical systems, stochastic flows, rough path, local times, interaction with analysis, mathematics of finance. |
Research students
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| Cisem Bektur |
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Random dynamical systems arising in models of financial markets. |
| Yuejiao Duan |
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SRB measures for random dynamical systems. |
| Samuel Durugo |
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Spectral properties of non-local operators through functional integration methods. |
| Paul Jones |
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Unitary double product integrals in quantum stochastic calculus as Bogolubov implementors. |
| Ye Luo |
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Stochastic partial differential equations. |
| McSylvester Omaba |
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| Kuanhou Tian |
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| Kenneth Uda |
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Stochastic dynamical systems. |
| Xince Wang |
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Weak solutions of forward and backward stochastic differential equations. |
| Qingfeng Wang |
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Properties of local times and applications. |
| Yue Wu |
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Random periodic solutions of stochastic differential equations. |
| Cyrus Yeadon |
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Random numerical dynamics for stochastic PDEs. |
| Lu Zhang |
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