Numerical Integration of Stochastic Differential Equations

di G.N. Milstein (Autore)

Springer, 2010

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.

• Autore: G.N. Milstein
• Editore: Springer
• Collana: Mathematics and Its Applications
• Anno: 2010
• Rilegatura: Paperback / softback
• Pagine: 172 p.
• Dimensioni: 235 x 155 mm
• EAN: 9789048144877

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