Stochastic functional differential equations driven by G-Browniain\n motion with monotone nonlinearity

2018/06/20 by Faiz Faizullah, Faizullah, Faiz
Economics, Econometrics and Finance · Mathematics · #34K50 #60H10 #60H20 #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1806.07824

openalex publication_date 2018/06/20 · openalex created_date 2022/08/29 · openalex updated_date 2026/07/28

Abstract

By using the Picard iteration scheme, this article establishes the existence\nand uniqueness theory for solutions to stochastic functional differential\nequations driven by G-Browniain motion. Assuming the monotonicity conditions,\nthe boundedness and existence-uniqueness results of solutions have been\nderived. The error estimation between Picard approximate solution y^k(t) and\nexact solution y(t) has been determined. The L²_G and exponential\nestimates have been obtained. The theory has been further generalized to weak\nmonotonicity conditions. The existence, uniqueness and exponential estimate\nunder the weak monotonicity conditions have been inaugurated.\n

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