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Concave and other generalizations of stochastic Gronwall inequalities

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arxiv 2204.06042 v2 pith:3ENMVJL4 submitted 2022-04-12 math.PR

Sarah Geiss This is my paper · ORCID
classification math.PR
keywords generalizationsgronwallinequalitiesscheutzowstochasticclassconcaveother
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We provide nonlinear generalizations of a class of stochastic Gronwall inequalities that have been studied by von Renesse and Scheutzow (2010), Scheutzow (2013), Xie and Zhang (2020) and Mehri and Scheutzow (2021). This class of stochastic Gronwall inequalities is a useful tool for SDEs. More precisely, we study generalizations of the Bihari-LaSalle type. Whilst in a closely connected article by the author convex generalizations are studied, we investigate here concave and other generalizations. These types of estimates are useful to obtain existence and uniqueness of global solutions of path-dependent SDEs driven by L\'evy processes under one-sided non-Lipschitz monotonicity and coercivity assumptions.

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Cited by 2 Pith papers

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    Random turbulent velocity fields cause generic scalar fields to dissipate energy and instantly regularize to sharp fractional regularity, with particle dispersion obeying t^{1/(1-alpha)}.

  2. Failure of the Weak Sard property without Anomalous Dissipation

    math.AP 2026-07 accept novelty 7.0 of 10

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