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 Blomker & J Duan); Asymptotics for a Space-Time Wigner Transform (L Borcea et al.); KdV Equation with Homogeneous Multiplicative Noise (A de Bouard & A Debussche); Stochastic Fractional Burgers Equation (Z Brze niak & L Debbi); Optimal Compensation of Executives (A Cadenillas et al.); The Freidlin-Wentzell LDP with Rapidly Growing Coefficients (P Chigansky & R Liptser); Convergence Rate of Weak Approximations (D Crisan & S Ghazali); Flow Properties of SDEs Driven by Fractional Brownian Motion (L Decreusefond & D Nualart); Regularity for Stochastic Navier-Stokes Equation (F Flandoli & M Romito); Rate of Convergence of Implicit Approximations (L Gyongy & A Millet); Maximum Principle for SPDEs (N V Krylov); Delay Estimation for Diffusion Processes (Yu A Kutoyants); Cauchy-Dirichlet Problem for an Integro-Differential Equation (R Mikulevicius & H Pragarauskas); Strict Solutions of Kolmogorov Equations (G Da Prato).