Volume 5, 2001
|Page(s)||261 - 297|
|Published online||15 August 2002|
Euler schemes and half-space approximation for the simulation of diffusion in a domain
École Polytechnique, Centre de Mathématiques Appliquées, 91128
Palaiseau Cedex, France; firstname.lastname@example.org.
Revised: 10 December 2001
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.
Mathematics Subject Classification: 35K20 / 60-08 / 60J60 / 65Cxx
Key words: Killed diffusion / reflected diffusion / discretization schemes / rates of convergence / weak approximation / boundary value problems for parabolic PDE.
© EDP Sciences, SMAI, 2001
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