Convergence of Weak Euler Approximation for Nondegenerate Stochastic Differential Equations Driven by Point and Martingale Measures

Remigijus Mikulevičius () and Changyong Zhang ()
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Remigijus Mikulevičius: University of Southern California
Changyong Zhang: Curtin University

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 43-80

Abstract: Abstract This paper studies the weak Euler approximation for solutions to stochastic differential equations (SDEs) driven by point and martingale measures, with Hölder-continuous coefficients. The equation under consideration includes a nondegenerate main part whose jump intensity measure is absolutely continuous with respect to the Lévy measure of a spherically symmetric stable process. It encompasses a broad range of stochastic processes including the nondegenerate diffusions and SDEs driven by Lévy processes. To investigate the dependence of the convergence rate on the regularity of the coefficients and driving processes, the regularity of a solution to the associated backward Kolmogorov equation is considered. In particular, for the first time the Hölder norm of the subordinated part of the corresponding generator is rigorously estimated.

Keywords: Stochastic differential equations; Point measure; Martingale measure; Weak Euler approximation; Rate of convergence; Hölder conditions; 60H30; 60H35; 60J60; 60J76 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01260-x

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