The Euler scheme for Lévy driven stochastic differential equations
type: Item
instance of: scholarly article
title: The Euler scheme for Lévy driven stochastic differential equations
zbMATH Open document ID: 0876.60030
author: Denis Talay
author: Philip Protter
published in: The Annals of Probability
publication date: 1997-11-18T00:00:00Z
review text: The paper considers the discrete time approximation of the solution of a stochastic differential equation that is driven by a Lévy process. It is shown that the Euler approximation converges under appropriate conditions in a weak sense to the solution of the given stochastic differential equation. If the Lévy measure has finite moments up to a certain order, then the typical rate of weak convergence has been shown. Otherwise the rate of convergence turns out to be smaller. The suggested Euler method is useful for Monte-Carlo simulation of solutions of specific integro-differential equations.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65C05
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 1018395
zbMATH Keywords: discrete time approximation
zbMATH Keywords: Lévy process
zbMATH Keywords: Euler approximation
zbMATH Keywords: Lévy measure
zbMATH Keywords: Monte-Carlo simulation
reviewed by: Eckhard Platen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1024404293
OpenAlex ID: W1996705901
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DOI: 10.1214/AOP/1024404293
description: scientific article; zbMATH DE number 1018395