Work

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

Year: 2021

Type: article

Abstract: There are numerous applications of the classical (deterministic) Gronwall inequality. Recently, Michael Scheutzow discovered a stochastic Gronwall inequality which provides upper bounds for p-th moments, p∈(0,1), of the supremum of nonnegative scalar continuous processes which satisfy a linear integral inequality. In this article we complement this with upper bounds for p-th moments, p∈[2,∞), of the supremum of general Itô processes which satisfy a suitable one-sided affine-linear growth condition. As example applications, we improve known results on strong local Lipschitz continuity in the starting point of solutions of stochastic differential equations (SDEs), on (exponential) moment estimates for SDEs, on strong completeness of SDEs, and on perturbation estimates for SDEs.

Source: Annales de l Institut Henri Poincaré Probabilités et Statistiques

DOI: 10.1214/20-aihp1064

Authors: Anselm Hudde, Martin Hutzenthaler, Sara Mazzonetto

Institutions: University of Duisburg-Essen, Institut Élie Cartan de Lorraine, Université de Lorraine

Language: French

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: Deutsche Forschungsgemeinschaft

Award: G5136792211