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

Emmanuel Gobet

ESAIM: Probability and Statistics (2001)

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

Abstract

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This paper is concerned with the problem of simulation of ( X t ) 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 (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 -

References

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