Numerical Integration of Stochastic Differential Equations
By: by G. N. Milstein
Series: Mathematics and Its Applications -- 313; Mathematics and Its Applications -- 313
Publisher: Springer Netherlands
Published: 1995
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] /
Number of pages: 172
ISBN-13: 9789048144877; 9789401584555
Subjects: Electronic data processing; Distribution (Probability theory); Computer science; Mathematics
Description: 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.
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