Details

Autor(en) / Beteiligte

• Milstein, G. N

Titel

Numerical Integration of Stochastic Differential Equations [Elektronische Ressource]

Ist Teil von

• Mathematics and Its Applications : 313

Ort / Verlag

Dordrecht : Springer Netherlands

Erscheinungsjahr

1995

Link zum Volltext

• Volltext

Link zu anderen Inhalten

• Volltext

Beschreibungen/Notizen

• U sing stochastic differential equations we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochastic 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 mathematical 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