Numerical Integration of Stochastic Differential Equations (Paperback)

G.N. Milstein

ISBN 10: 9048144876 / ISBN 13: 9789048144877

Published by Springer, Dordrecht, 2010

About this Item

Paperback. 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. U sing stochastic differential equations we can successfully model systems that funcA tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochasA tic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in mathA ematical physics involve 'damned dimensions', of ten leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which of ten come about as characteristics. In its simplest form, the method of characteristics is as follows. Consider a system of n ordinary differential equations dX = a(X) dt. (O.l ) Let Xx(t) be the solution of this system satisfying the initial condition Xx(O) = x. For an arbitrary continuously differentiable function u(x) we then have: (0.2) u(Xx(t)) - u(x) = j (a(Xx(t)), ~~ (Xx(t))) Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

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Bibliographic Details

• Title: Numerical Integration of Stochastic Differential Equations (Paperback)
• Publisher: Springer, Dordrecht
• Publication Date: 2010
• Language: English
• ISBN 10: 9048144876
• ISBN 13: 9789048144877
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

Language Notes

Text: English (translation)
Original Language: Russian