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The Euler scheme for a stochastic differential equation driven by pure jump semimartingales. (English) Zbl 1322.65019

Summary: In this paper, we propose the asymptotic error distributions of the Euler scheme for a stochastic differential equation driven by Itô semimartingales. J. Jacod [Ann. Probab. 32, No. 3A, 1830–1872 (2004; Zbl 1054.65008)] studied this problem for stochastic differential equations driven by pure jump Lévy processes and obtained quite sharp results. We extend his results to a more general pure jump Itô semimartingale.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60G48 Generalizations of martingales
60J75 Jump processes (MSC2010)
60F17 Functional limit theorems; invariance principles

Citations:

Zbl 1054.65008
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