Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications, 313)

Milstein, G.N.

ISBN 10: 079233213X / ISBN 13: 9780792332138

Verlag: Springer, 1994

In. Bestandsnummer des Verkäufers ria9780792332138_new

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.

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.

Bibliografische Details

Titel: Numerical Integration of Stochastic ...
Verlag: Springer
Erscheinungsdatum: 1994
Einband: Hardcover
Zustand: New