Stochastic Volterra integral equations driven by $ G $-Brownian motion

Bingru Zhao; Renxing Li; Mingshang Hu

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arXiv · 2504.21293

Stochastic Volterra integral equations driven by $ G $-Brownian motion

Bingru Zhao·Renxing Li·Mingshang Hu

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Abstract

In this paper, we study the stochastic Volterra integral equation driven by $G$-Brownian motion ($G$-SVIE). The existence, uniqueness and two types of continuity of the solution to $G$-SVIE are obtained. Moreover, combining a new quasilinearization technique with the two-step approximation method, we establish the corresponding comparison theorem for a class of $G$-SVIEs. In particular, by means of this method, the classical assumptions on partial derivatives of the coefficients are unnecessary.

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BibTeX RIS

Bingru Zhao, Renxing Li, Mingshang Hu. 2025-04-30. Stochastic Volterra integral equations driven by $ G $-Brownian motion. https://arxiv.org/abs/2504.21293

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