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Numerical Integration of Stochastic Differential Equations 1995th Edition
Author(s): G.N. Milstein (Author)
- Publisher: Springer
- Publication Date: November 30, 1994
- Edition: 1995th
- Language: English
- Print length: 180 pages
- ISBN-10: 079233213X
- ISBN-13: 9780792332138
Book Description
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.
