Euler schemes and half-space approximation for the simulation of diffusion in a domain
ESAIM: Probability and Statistics, Tome 5 (2001), pp. 261-297.

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
Mots clés : killed diffusion, reflected diffusion, discretization schemes, rates of convergence, weak approximation, boundary value problems for parabolic PDE 
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     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},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2001},
     mrnumber = {1889160},
     zbl = {0998.60081},
     language = {en},
     url = {http://www.numdam.org/item/PS_2001__5__261_0/}
}
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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://www.numdam.org/item/PS_2001__5__261_0/

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