On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes

Remigijus Mikulevičius; Changyong Zhang

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arXiv · 1007.2914

On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes

Remigijus Mikulevičius·Changyong Zhang

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Abstract

The paper studies the rate of convergence of the weak Euler approximation for It\^{o} diffusion and jump processes with H\"{o}lder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in H\"{o}lder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.

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Remigijus Mikulevičius, Changyong Zhang. 2010-07-17. On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\^{o} Diffusion and Jump Processes. https://arxiv.org/abs/1007.2914

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