# Euler schemes and half-space approximation for the simulation of diffusion in a domain

ESAIM: Probability and Statistics (2001)

- Volume: 5, page 261-297
- ISSN: 1292-8100

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topGobet, Emmanuel. "Euler schemes and half-space approximation for the simulation of diffusion in a domain." ESAIM: Probability and Statistics 5 (2001): 261-297. <http://eudml.org/doc/104277>.

@article{Gobet2001,

abstract = {This paper is concerned with the problem of simulation of $(X_t)_\{0\le t\le T\}$, 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 $\partial D$ 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.},

author = {Gobet, Emmanuel},

journal = {ESAIM: Probability and Statistics},

keywords = {killed diffusion; reflected diffusion; discretization schemes; rates of convergence; weak approximation; boundary value problems for parabolic PDE; boundary value problems for parabolic partial differential equations},

language = {eng},

pages = {261-297},

publisher = {EDP-Sciences},

title = {Euler schemes and half-space approximation for the simulation of diffusion in a domain},

url = {http://eudml.org/doc/104277},

volume = {5},

year = {2001},

}

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

PB - EDP-Sciences

VL - 5

SP - 261

EP - 297

AB - This paper is concerned with the problem of simulation of $(X_t)_{0\le t\le T}$, 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 $\partial D$ 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.

LA - eng

KW - killed diffusion; reflected diffusion; discretization schemes; rates of convergence; weak approximation; boundary value problems for parabolic PDE; boundary value problems for parabolic partial differential equations

UR - http://eudml.org/doc/104277

ER -

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