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First time to exit of a continuous Itȏ process: General moment estimates and L₁-convergence rate for discrete time approximations
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First time to exit of a continuous Itȏ process: General moment estimates and L₁-convergence rate for discrete time approximations
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Journal Article
First time to exit of a continuous Itȏ process: General moment estimates and L₁-convergence rate for discrete time approximations
2017
Overview
We establish general moment estimates for the discrete and continuous exit times of a general It₁ process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the approximation of a continuous exit time by a discrete counterpart, computed on a grid. In particular, we prove that the discrete exit time of the Euler scheme of a diffusion converges in the L₁ norm with an order 1/2 with respect to the mesh size. This rate is optimal.
Publisher
International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability,Bernoulli Society for Mathematical Statistics and Probability
Subject
