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

Emmanuel Gobet

ESAIM: Probability and Statistics (2010)

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

Abstract

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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.

How to cite

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Gobet, 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 -

References

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