Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications)

G.N. Milstein

ISBN 10: 9048144876 / ISBN 13: 9789048144877

Verlag: Springer Netherlands, 1995

Beschreibung

184 pages. 9.25x6.10x0.41 inches. In Stock. Bestandsnummer des Verkäufers x-9048144876

Bibliografische Details

Titel: Numerical Integration of Stochastic ...

Verlag: Springer Netherlands

Erscheinungsdatum: 1995

Einband: Paperback

Zustand: Brand New

Über diesen Titel

Reseña del editor:

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.