Geodesic
Euler schemes and half-space approximation for the simulation of diffusion in a domain
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 261-297 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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.

Classification : 35K20, 60-08, 60J60, 65Cxx
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},
     year = {2001},
     publisher = {EDP-Sciences},
     volume = {5},
     mrnumber = {1889160},
     zbl = {0998.60081},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/item/PS_2001__5__261_0/
LA  - en
ID  - PS_2001__5__261_0
ER  - 
%0 Journal Article
%A Gobet, Emmanuel
%T Euler schemes and half-space approximation for the simulation of diffusion in a domain
%J ESAIM: Probability and Statistics
%D 2001
%P 261-297
%V 5
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/item/PS_2001__5__261_0/
%G en
%F PS_2001__5__261_0
Gobet, Emmanuel. Euler schemes and half-space approximation for the simulation of diffusion in a domain. ESAIM: Probability and Statistics, Tome 5 (2001), pp. 261-297. http://geodesic.mathdoc.fr/item/PS_2001__5__261_0/