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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Format: | Article |
Language: | English |
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Wiley
2014-01-01
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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. |
format | Article |
id | doaj-art-b1454923d1304f9cb2b01f0f54af585f |
institution | Kabale University |
issn | 1085-3375 1687-0409 |
language | English |
publishDate | 2014-01-01 |
publisher | Wiley |
record_format | Article |
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 |