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killed diffusion

ESAIM: Probability and Statistics (1)

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Euler schemes and half-space approximation for the simulation of diffusion in a domain
Emmanuel Gobet
Journal:

ESAIM: Probability and Statistics / Volume 5 / 2001

Published online by Cambridge University Press:

15 August 2002, pp. 261-297

Print publication:

2001
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This paper is concerned with the problem of simulation of (Xt)0≤t≤T , thesolution of a stochastic differential equation constrained by some boundary conditions in a smooth domainD: namely, we consider the case where the boundary ∂D is killing, or where it is instantaneouslyreflecting 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 orderN -1 under some conditions. The construction of these schemes is based on a natural principle of localapproximation of the domain into a half space, for which efficient simulations are available.