Stochastic differential equations : theory and applications (Interdiscipline mathematical sciences, Vol. 2)

This volume consists of 15 articles written by experts in stochastic analysis. The first paper in the volume, Stochastic Evolution Equations by N V Krylov and B L Rozovskii, was originally published in Russian in 1979. After more than a quarter-century, this paper remains a standard reference in the field of stochastic partial differential equations (SPDEs) and continues to attract the attention of mathematicians of all generations. Together with a short but thorough introduction to SPDEs, it presents a number of optimal, and essentially unimprovable, results about solvability for a large class of both linear and non-linear equations. The other papers in this volume were specially written for the occasion of Prof Rozovskii's 60th birthday. They tackle a wide range of topics in the theory and applications of stochastic differential equations, both ordinary and with partial derivatives.

Stochastic Evolution Equations (N V Krylov & B L Rozovskii). Predictability of the Burgers Dynamics Under Model Uncertainty (D Blömker & J Duan). Asymptotics for the Space-Time Wigner Transform with Applications to Imaging (L Borcea et al.). The Korteweg-de Vries Equation with Multiplicative Homogeneous Noise (A de Bouard & A Debussche). On Stochastic Burgers Equation Driven by a Fractional Laplacian and Space-Time White Noise (Z Brzezniak & L Debbi). Stochastic Control Methods for the problem of Optimal Compensation of Executives (A Cadenillas et al.). The Freidlin-Wentzell LDP with Rapidly Growing Coefficients (P Chigansky & R Liptser). On the Convergence Rates of a General Class of Weak Approximations of SDEs (D Crisan & S Ghazali). Flow Properties of Differential Equations Driven by Fractional Brownian Motion (L Decreusefond & D Nualart). Regularity of Transition Semigroups Associated to a 3D Stochastic Navier-Stokes Equation (F Flandoli & M Romito). Rate of Convergence of Implicit Approximations for Stochastic Evolution Equations (I Gyöngy & A Millet). Maximum Principle for SPDEs and Its Applications (N V Krylov). On Delay Estimation and Testing for Diffusion Type Processes (Yu A Kutoyants). On Cauchy-Dirichlet Problem for Linear Integro-Differential Equation in Weighted Sobolev Spaces (R Mikulevicius & H Pragarauskas). Strict Solutions of Kolmogorov Equations in Hilbert Spaces and Applications (G Da Prato).