عنوان

Numerical Integration of Stochastic Differential Equations

(Number (ISBN

9789048144877

(Number (ISBN

9789401584555

Number

b408361

Title Proper

Numerical Integration of Stochastic Differential Equations

General Material Designation

[Book]

First Statement of Responsibility

by G. N. Milstein.

Place of Publication, Distribution, etc.

Dordrecht :

Name of Publisher, Distributor, etc.

Imprint: Springer,

Date of Publication, Distribution, etc.

1995.

Series Title

Mathematics and Its Applications ;

Volume Designation

313

Text of Note

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.

0

Text of Note

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.

International Standard Book Number

9789048144877

Title

Springer eBooks

Computer science.

Distribution (Probability theory).

Electronic data processing.

Mathematics.

Milʹshteĭn, G. N., (Grigoriĭ Noĭkhovich)

SpringerLink (Online service)

Date of Transaction

20190307160400.0

Electronic name

[Book]

Y