A stochastic Gronwall inequality and applications to moments, strong completeness, strong local Lipschitz continuity, and perturbations

DOI10.1214/20-AIHP1064zbMath1491.60082arXiv1903.08727OpenAlexW3162662965MaRDI QIDQ2041810

Anselm Hudde, Martin Hutzenthaler, Sara Mazzonetto

Publication date: 23 July 2021

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.08727

zbMATH Keywords

perturbation theoryexponential momentsmartingale inequalitystrong completenessstochastic Gronwall lemmastochastic Gronwall inequalitystrong local Lipschitz continuity

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items (5)

Strong convergence rate of Euler-Maruyama approximations in temporal-spatial Hölder-norms ⋮ A note on the stochastic version of the Gronwall lemma ⋮ A Kolmogorov-Chentsov type theorem on general metric spaces with applications to limit theorems for Banach-valued processes ⋮ Sharp convex generalizations of stochastic Gronwall inequalities ⋮ Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven stochastic differential equations with smooth drift coefficient functions with at most polynomially growing derivatives

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