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
Euler scheme for reflected stochastic differential equations
✍ Scribed by D. Lépingle
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 309 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0378-4754
No coin nor oath required. For personal study only.
✦ Synopsis
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 permet de simuler les solutions d'6quations diff6rentielles stochastiques r6fl6chies sur des hyperplans parall~les aux axes avec le mSme ordre de convergence qu'en absence de r6flexion.
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