Numerical Integration of Stochastic Differ...

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Beschreibung

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.

Inhaltsverzeichnis

1. Mean-square approximation of solutions of systems of stochastic differential equations.- 2. Modeling of Itô integrals.- 3. Weak approximation of solutions of systems of stochastic differential equations.- 4. Application of the numerical integration of stochastic equations for the Monte-Carlo computation of Wiener integrals.

Erscheinungsjahr:	1994
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	viii 172 S. 1 s/w Illustr.
ISBN-13:	9780792332138
ISBN-10:	079233213X
Sprache:	Englisch
Einband:	Gebunden
Autor:	Milstein, G. N.
Hersteller:	Springer Netherland Springer Netherlands
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	241 x 160 x 15 mm
Von/Mit:	G. N. Milstein
Erscheinungsdatum:	30.11.1994
Gewicht:	0,448 kg