Paper Information

Journal:   JOURNAL OF MATHEMATICAL EXTENSION   2018 , Volume 12 , Number 3; Page(s) 33 To 53.
 
Paper: 

Convergence of Euler-Maruyama Method for Stochastic Differential Equations Driven by 􀀀 stable Lé vy Motion

 
 
Author(s):  TARAMI BAHRAM*, Avaji Mohsen
 
* Department of Statistics, College of sciences, Shiraz university, Shiraz, Iran
 
Abstract: 
In the literature, the Euler-Maruyama (EM) method for approximation purposes of stochastic differential Equations (SDE) driven by -stable Lé vy motions is reported. Convergence in probability of that method was proven but it is surrounded by some ambiguities. To accomplish the but without ambiguities, this article has derived convergence in probability of numerical EM method based on diffusion given by semimartingales for SDEs driven by -stable processes. Some examples are provided, their numerical solution are obtained and theoretical results are reconfirmed. The adopted method could be applied to other subclasses of semimartingales.
 
Keyword(s): Semimartingale,Stochastic differential equation,Euler-Maruyama method, ,􀀀,stable Lé,vy processes,Convergence in probability
 
References: 
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