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Paper No. 08-18

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S Peluchetti, GO Roberts and B Casella

The strong weak convergence of the Quasi-EA

Date: January 2008

Abstract: In this paper we investigate the convergence of a novel simulation scheme to the target diffusion process. This scheme, the Quasi-EA, is closely related to the Exact Algorithm (EA) for diffusion processes, as it is obtained by neglecting the rejection step in EA. We prove the existence of a myopic coupling between the Quasi-EA and the diffusion. Moreover, an upper bound for the coupling probability is given. Consequently, we establish the convergence of the Quasi-EA to the diffusion with respect to the total variation distance.