Numerical Integration of Stochastic Differential Equations - Mathematics and Its Applications - G.n. Milstein - Books - Springer - 9789048144877 - December 3, 2010
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Numerical Integration of Stochastic Differential Equations - Mathematics and Its Applications 1st Ed. Softcover of Orig. Ed. 1995 edition

G.n. Milstein

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Numerical Integration of Stochastic Differential Equations - Mathematics and Its Applications 1st Ed. Softcover of Orig. Ed. 1995 edition

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.


172 pages, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released December 3, 2010
ISBN13 9789048144877
Publishers Springer
Pages 172
Dimensions 155 × 235 × 9 mm   ·   263 g
Language English