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Article Dans Une Revue Stochastic Processes and their Applications Année : 2023

Perturbations of singular fractional SDEs

Résumé

We obtain well-posedness results for a class of ODE with a singular drift and additive fractional noise, whose right-hand-side involves some bounded variation terms depending on the solution. Examples of such equations are reflected equations, where the solution is constrained to remain in a rectangular domain, as well as so-called perturbed equations, where the dynamics depend on the running extrema of the solution. Our proof is based on combining the Catellier-Gubinelli approach based on Young nonlinear integration, with some Lipschitz estimates in $p$-variation for maps of Skorokhod type, due to Falkowski and S{\l}ominski. An important step requires to prove that fractional Brownian motion, when perturbed by sufficiently regular paths (in the sense of $p$-variation), retains its regularization properties. This is done by applying a variant of the stochastic sewing lemma.

Dates et versions

hal-03867151 , version 1 (23-11-2022)

Identifiants

Citer

Paul Gassiat, Łukasz Mądry. Perturbations of singular fractional SDEs. Stochastic Processes and their Applications, 2023, 161, pp.137-172. ⟨10.1016/j.spa.2023.04.004⟩. ⟨hal-03867151⟩
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