Numerical Integration of Stochastic Differential Equations

Milstein, Grigori N.

ISBN 10: 079233213X / ISBN 13: 9780792332138

Verlag: Springer, 1994

Beschreibung

Bestandsnummer des Verkäufers 1212170-n

Bibliografische Details

• Titel: Numerical Integration of Stochastic Differential Equations
• Verlag: Springer
• Erscheinungsjahr: 1994
• Sprache: Englisch
• ISBN-10: 079233213X
• ISBN-13: 9780792332138
• Einband: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

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.