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<p>We prove global uniqueness and input–output continuity for a nonlinear stochastic fractional differential equation. Following conjectures of a recent contribution, the noise’s intensity can be state-dependent here, for certain non-integer orders. We employ Grönwall-type inequalities with an adequate weighted norm for continuous processes, instead of recursive arguments or fixed-point results.</p>

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On the well-posedness problem for a stochastic fractional differential equation using weighted norms

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Marc Jornet

摘要

We prove global uniqueness and input–output continuity for a nonlinear stochastic fractional differential equation. Following conjectures of a recent contribution, the noise’s intensity can be state-dependent here, for certain non-integer orders. We employ Grönwall-type inequalities with an adequate weighted norm for continuous processes, instead of recursive arguments or fixed-point results.