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Weak approximation of killed diffusion using Euler schemes

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  • Gobet, Emmanuel

Abstract

We study the weak approximation of a multidimensional diffusion (Xt)0[less-than-or-equals, slant]t[less-than-or-equals, slant]T killed as it leaves an open set D, when the diffusion is approximated by its continuous Euler scheme or by its discrete one , with discretization step T/N. If we set [tau] := inf{t>0: Xt[negated set membership]D} and , we prove that the discretization error can be expanded to the first order in N-1, provided support or regularity conditions on f. For the discrete scheme, if we set , the error is of order N-1/2, under analogous assumptions on f. This rate of convergence is actually exact and intrinsic to the problem of discrete killing time.

Suggested Citation

  • Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
    • Handle: RePEc:eee:spapps:v:87:y:2000:i:2:p:167-197
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    References listed on IDEAS

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    1. BALLY Vlad & TALAY Denis, 1996. "The Law of the Euler Scheme for Stochastic Differential Equations: II. Convergence Rate of the Density," Monte Carlo Methods and Applications, De Gruyter, vol. 2(2), pages 93-128, December.
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