Euler schemes and half-space approximation for the simulation of diffusion in a domain
Open Access
- 1 January 2001
- journal article
- research article
- Published by EDP Sciences in ESAIM: Probability and Statistics
- Vol. 5, 261-297
- https://doi.org/10.1051/ps:2001112
Abstract
This paper is concerned with the problem of simulation of (Xt)0≤t≤T , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain D: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneously reflecting in an oblique direction. Given N discretization times equally spaced on the interval [0,T], we propose new discretization schemes: they are fully implementable and provide a weak error of order N -1 under some conditions. The construction of these schemes is based on a natural principle of local approximation of the domain into a half space, for which efficient simulations are available.Keywords
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