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

Emmanuel Gobet (2001)

ESAIM: Probability and Statistics

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...

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

Emmanuel Gobet (2010)

ESAIM: Probability and Statistics

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....

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