Professor and Distinguished Scholar; Ph.D., University of Warwick, England, 1976. Stochastic analysis, deterministic and stochastic hereditary dynamical systems, probabilistic analysis of PDEs, Malliavin calculus, stochastic numerics, stochastic PDEs.
I have worked in the following areas:
- Deterministic Functional Differential Equations on Manifolds
- Stochastic Systems with Memory
- The Malliavin Calculus. Hypoellipticity
- Finite-dimensional Stochastic Flows. The Stable Manifold Theorem
- Stochastic Numerics and Finance
- Infinite-dimensional Stochastic Dynamical Systems
- Stochastic Partial Differential Equations
- An Extension of Hörmander's Theorem for Infinitely Degenerate Second-Order Operators, with Denis Bell, Duke Mathematical Journal, Vol.78, No. 3, (1995), 453-475.
- Lyapunov Exponents of Linear and Stochastic Functional Differential Equations Driven by Semimartingales, Part I: The Multiplicative Ergodic Theory, with M. Scheutzow, Annals of Institute of Henri Poincaré, Probabilites and Statistiques Vol. 32, 1, (1996), 69-105.
- Lyapunov Exponents of Linear Stochastic Functional Differential Equations, Part II: Examples and Case Studies, With M. Scheutzow, (preprint 1995) The Annals of Probability , Vol. 25, No. 3, (1997), 1210-1240.
- Stochastic Differential Systems with Memory: Theory, Examples and Applications, Stochastic Analysis and Related Topics VI. The Geilo Workshop, 1996, ed. L. Decreusefond, Jon Gjerde, B. Øksendal, A.S. Üstünel, Progress in Probability, Birkhäuser (1998), 1-77.
- The Stable Manifold Theorem for Stochastic Differential Equations, with M. Scheutzow, The Annals of Probability, Vol. 27, No. 2, (1999), 615-652.
- The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory I: Existence of the Semiflow, with M.K.R. Scheutzow, Journal of Functional Analysis, 205, (2003), 271-305 (communicated by L. Gross)
- The Stable Manifold Theorem for Nonlinear Stochastic Systems with Memory II: The Local Stable Manifold Theorem, with M.K.R. Scheutzow, Journal of Functional Analysis, 206, (2004), 253-306 (communicated by L. Gross)
- The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations. Part 1: The Stochastic Semiflow ", Part 2: Existence of stable and unstable manifolds", with Tusheng Zhang and Huaizhong Zhao, Memoirs of the American Mathematical Society, Volume 196, 2008; 105 pp; ISBN-10: 0-8218-4250-1