𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The Euler scheme for Hilbert space valued stochastic differential equations

✍ Scribed by Raúl Fierro; Soledad Torres


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
93 KB
Volume
51
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis


Here we consider stochastic di erential equations whose solutions take values in a Hilbert space. The Euler Scheme for approximating these solutions is used, and the global error is estimated. In addition, solutions are approximated by means of a process which takes values in a ÿnite-dimensional subspace.


📜 SIMILAR VOLUMES


Euler scheme for reflected stochastic di
✍ D. Lépingle 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 309 KB

Using some exponential variables in the time discretization of some reflected stochastic differential equations yields the same rate of convergence as in the usual Euler-Maruyama scheme. L'utilisation ~ chaque pas d'une nouvelle variable exponentielle ind6pendante des accroissements browniens perme

The Euler scheme for stochastic differen
✍ Vlad Bally; Denis Talay 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 304 KB

We study the approximation problem of Ef(Xr) by Ef(X~.), where (Xt) is the solution of a stochastic differential equation, (X~) is defined by the Euler discretization scheme with step T/n, and f is a given function. For smooth f's, Talay and Tubaro had shown that the error Ef(Xr) -Ef(X~) can be expa

Invariant measures for dichotomous stoch
✍ Onno Van Gaans; Sjoerd Verduyn Lunel 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 80 KB

We study existence of invariant measures for semilinear stochastic differential equations in Hilbert spaces. We consider infinite dimensional noise that is white in time and colored in space and we assume that the nonlinearities are Lipschitz continuous. We show that if the equation is dichotomous i