This paper is concerned with the problem of simulation of , the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain : namely, we consider the case where the boundary is killing, or where it is instantaneously reflecting in an oblique direction. Given discretization times equally spaced on the interval , we propose new discretization schemes: they are fully implementable and provide a weak error of order 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: killed diffusion, reflected diffusion, discretization schemes, rates of convergence, weak approximation, boundary value problems for parabolic PDE
@article{PS_2001__5__261_0, author = {Gobet, Emmanuel}, title = {Euler schemes and half-space approximation for the simulation of diffusion in a domain}, journal = {ESAIM: Probability and Statistics}, pages = {261--297}, publisher = {EDP-Sciences}, volume = {5}, year = {2001}, mrnumber = {1889160}, zbl = {0998.60081}, language = {en}, url = {http://www.numdam.org/item/PS_2001__5__261_0/} }
TY - JOUR AU - Gobet, Emmanuel TI - Euler schemes and half-space approximation for the simulation of diffusion in a domain JO - ESAIM: Probability and Statistics PY - 2001 SP - 261 EP - 297 VL - 5 PB - EDP-Sciences UR - http://www.numdam.org/item/PS_2001__5__261_0/ LA - en ID - PS_2001__5__261_0 ER -
Gobet, Emmanuel. Euler schemes and half-space approximation for the simulation of diffusion in a domain. ESAIM: Probability and Statistics, Volume 5 (2001), pp. 261-297. http://www.numdam.org/item/PS_2001__5__261_0/
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