Numerical Integration of Stochastic Differential Equations

G. N. Milstein

ISBN 10: 079233213X / ISBN 13: 9780792332138

Published by Springer Netherlands, Springer Netherlands, 1994

About this Item

Druck auf Anfrage Neuware - Printed after ordering - U sing stochastic differential equations we can successfully model systems that func tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas 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 math 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))) dt.

Seller Inventory # 9780792332138

Bibliographic Details

• Title: Numerical Integration of Stochastic Differential Equations
• Publisher: Springer Netherlands, Springer Netherlands
• Publication Date: 1994
• Language: English
• ISBN 10: 079233213X
• ISBN 13: 9780792332138
• Binding: Buch
• Condition: Neu
• Dimensions: 241W x 160H x 15D millimeters 241 millimeters width by 160 millimeters height by 15 millimeters depth
• Weight: 448 grams

About this title

Synopsis

U sing stochastic differential equations we can successfully model systems that func- tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas- 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 math- 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))) dt.

Language Notes

Text: English (translation)
Original Language: Russian