Devoted to meansquare and weak approximation of solutions of stochastic differential equations, the approximations being two fundamental aspects in the contemporary theory of such equations. Solutions provided by numerical methods serve as characteristics for a number of mathematical physics problems, and the probability representations can combine with a Monte-Carlo method to reduce complex multidimensional problems of mathematical physics to the integration of stochastic equations. Translated from the 1988 Russian edition. Annotation copyright Book News, Inc. Portland, Or.
This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.
