Improved convergence rate for the simulation of stochastic differential equations driven by subordinated Levy processes

S Rubenthaler, Magnus Wiktorsson

Research output: Contribution to journalArticlepeer-review

4 Citations (SciVal)

Abstract

We consider the Euler approximation of stochastic differential equations (SDEs) driven by Levy processes in the case where we cannot simulate the increments of the driving process exactly. In some cases, where the driving process Y is a subordinated stable process, i.e., Y = Z(V) with V a subordinator and Z a stable process, we propose an approximation Y by Z(V-n) where V-n is an approximation of V. We then compute the rate of convergence for the approximation of the solution X of an SDE driven by Y using results about the stability of SDEs. (C) 2003 Elsevier B.V. All rights reserved.
Original languageEnglish
Pages (from-to)1-26
JournalStochastic Processes and their Applications
Volume108
Issue number1
DOIs
Publication statusPublished - 2003

Subject classification (UKÄ)

  • Probability Theory and Statistics

Keywords

  • rate
  • convergence
  • stochastic differential equation
  • numerical approximation
  • Levy process
  • shot noise representation
  • subordination

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