Existence-Uniqueness and p-Moment Estimates of Solutions to Nonlinear G-Stochastic Differential Equations

Rahman Ullah, Kinza Manzoor, Faiz Faizullah, Rashid Ali, Ibraheem M. Alsulami and Amer Alsulami

Journal of Mathematics, 2026, vol. 2026, 1-12

Abstract: This article presents the analysis for solutions to nonlinear G-stochastic differential equations (GSDEs). The uniqueness of solutions has been determined under the semimonotonicity criterion which generalize to a much broader class of coefficients and is central to modern stochastic analysis. The existence of solutions has been proven via the Yosida approximation scheme. The proofs of our results depend on the properties of subexpectation, with key applications of the Hölder, Gronwall, and Burkholder–Davis–Gundy (BDG) inequalities. We demonstrate that the Yosida approximate solutions are bounded and converge to the unique solution of the GSDEs. The pth moment exponential estimate has been investigated. An illustrative example is also provided.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:9016420

DOI: 10.1155/jom/9016420

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