Articlebronze2011

Strong solutions for stochastic differential equations with jumps

83 citations0/0 files storedAnnales de l Institut Henri Poincaré Probabilités et Statistiques

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Stochastic processes and financial applications Nonlinear Differential Equations Analysis Stochastic processes and statistical mechanics

Abstract

Nous étudions des équations stochastiques générales avec sauts et proposons un critère qui garantit l’existence et l’unicité de solutions fortes sous des conditions de régularité de type Yamada–Watanabe. Les résultats sont appliqués à des équations stochastiques conduites par des processus de Lévy de sauts positifs.

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1983Stochastic Differential Equations and Diffusion Processes 1971On the uniqueness of solutions of stochastic differential equations

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2013Stochastic differential equations with Sobolev drifts and driven by $\alpha$-stable processes 2012Strong solutions of jump-type stochastic equations 2018Jump type stochastic differential equations with non-Lipschitz coefficients: Non-confluence, Feller and strong Feller properties, and exponential ergodicity 2015Yamada-Watanabe Results for Stochastic Differential Equations with Jumps 2013On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes 2020Strong existence and uniqueness for stable stochastic differential equations with distributional drift 2019Regime-Switching Jump Diffusions with Non-Lipschitz Coefficients and Countably Many Switching States: Existence and Uniqueness, Feller, and Strong Feller Properties

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