Numerical Integration of Stochastic Differential Equations

G.N. Milstein (Autor)

Buch | Softcover

172 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1995
Springer (Verlag)
978-90-481-4487-7 (ISBN)

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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.

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.

Erscheint lt. Verlag	3.12.2010
Reihe/Serie	Mathematics and Its Applications ; 313
Zusatzinfo	VIII, 172 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	90-481-4487-6 / 9048144876
ISBN-13	978-90-481-4487-7 / 9789048144877
Zustand	Neuware