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A uniqueness criterion for McKean–Vlasov fractional stochastic differential equations in Lp

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  • Pourhadi, Ehsan
  • Li, Chenkuan

Abstract

In this article, we establish a uniqueness criterion for McKean–Vlasov nonlinear stochastic differential equations in Lp, driven by Brownian motion. This is achieved using a combination of Nagumo-type and Osgood conditions. The main contribution of this paper is to unify various existing uniqueness theorems. Specifically, we extend the classical Lipschitz uniqueness theorem and incorporate recent results for ordinary differential equations in the case where p=2, α=1, and distribution terms are omitted. Moreover, our methodology is applicable to nonlinear fractional stochastic differential equations (FSDEs). To demonstrate the applicability of our main result, we present numerical examples that support the theoretical findings.

Suggested Citation

  • Pourhadi, Ehsan & Li, Chenkuan, 2025. "A uniqueness criterion for McKean–Vlasov fractional stochastic differential equations in Lp," Chaos, Solitons & Fractals, Elsevier, vol. 200(P3).
    • Handle: RePEc:eee:chsofr:v:200:y:2025:i:p3:s096007792501166x
    DOI: 10.1016/j.chaos.2025.117153
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    References listed on IDEAS

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    1. A. A. Elmandouh & M. E. Elbrolosy & Ram Jiwari, 2022. "Integrability, Variational Principle, Bifurcation, and New Wave Solutions for the Ivancevic Option Pricing Model," Journal of Mathematics, Hindawi, vol. 2022, pages 1-15, September.
    2. Alexander Kalinin & Thilo Meyer-Brandis & Frank Proske, 2024. "Stability, Uniqueness and Existence of Solutions to McKean–Vlasov Stochastic Differential Equations in Arbitrary Moments," Journal of Theoretical Probability, Springer, vol. 37(4), pages 2941-2989, November.
    3. Lei Fan & Justin Sirignano, 2024. "Machine Learning Methods for Pricing Financial Derivatives," Papers 2406.00459, arXiv.org.
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