Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme

We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions Xk of G-SFDEs are given. We show that the unique...

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Main Author: Faiz Faizullah
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/809431
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author Faiz Faizullah
author_facet Faiz Faizullah
author_sort Faiz Faizullah
collection DOAJ
description We present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions Xk of G-SFDEs are given. We show that the unique solution of G-SFDEs gets convergence from Cauchy-Maruyama (CM) approximate solutions. The existence theorem for G-SFDEs is developed with the above mentioned scheme.
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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
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series Abstract and Applied Analysis
spelling doaj-art-b1454923d1304f9cb2b01f0f54af585f2025-02-03T05:58:49ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/809431809431Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation SchemeFaiz Faizullah0Department of Basic Sciences and Humanities, College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), PakistanWe present the Cauchy-Maruyama (CM) approximation scheme and establish the existence theory of stochastic functional differential equations driven by G-Brownian motion (G-SFDEs). Several useful properties of Cauchy-Maruyama (CM) approximate solutions Xk of G-SFDEs are given. We show that the unique solution of G-SFDEs gets convergence from Cauchy-Maruyama (CM) approximate solutions. The existence theorem for G-SFDEs is developed with the above mentioned scheme.http://dx.doi.org/10.1155/2014/809431
spellingShingle Faiz Faizullah
Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
Abstract and Applied Analysis
title Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
title_full Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
title_fullStr Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
title_full_unstemmed Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
title_short Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme
title_sort existence of solutions for g sfdes with cauchy maruyama approximation scheme
url http://dx.doi.org/10.1155/2014/809431
work_keys_str_mv AT faizfaizullah existenceofsolutionsforgsfdeswithcauchymaruyamaapproximationscheme