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

ESAIM: Probability and Statistics (2010)

- 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 (2010): 261-297. <http://eudml.org/doc/197733>.

@article{Gobet2010,

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. },

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.; killed diffusion; weak approximation; boundary value problems for parabolic partial differential equations},

language = {eng},

month = {3},

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/197733},

volume = {5},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 5

SP - 261

EP - 297

AB -
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.

LA - eng

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

UR - http://eudml.org/doc/197733

ER -

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