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

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  • Faiz Faizullah

Abstract

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 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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  • Faiz Faizullah, 2014. "Existence of Solutions for G-SFDEs with Cauchy-Maruyama Approximation Scheme," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, September.
    • Handle: RePEc:hin:jnlaaa:809431
    DOI: 10.1155/2014/809431
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    Cited by:

    1. Rahman Ullah & Faiz Faizullah & Quanxin Zhu, 2024. "The Convergence and Boundedness of Solutions to SFDEs with the G-Framework," Mathematics, MDPI, vol. 12(2), pages 1-12, January.

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