Work

Regularization of multiplicative SDEs through additive noise

Year: 2022

Type: article

Abstract: We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the program of regularization by noise to the case of multiplicative SDEs. Our method relies on a combination of the nonlinear Young formalism developed by Catellier and Gubinelli (Stochastic Process. Appl. 126 (2016) 2323–2366), and stochastic averaging estimates recently obtained by Hairer and Li (Ann. Probab. 48 (2020) 1826–1860).

Source: The Annals of Applied Probability

DOI: 10.1214/21-aap1778

Authors: Lucio Galeati, Fabian A. Harang

Institutions: University of Bonn, University of Oslo

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funders: Deutsche Forschungsgemeinschaft, Norges Forskningsråd

Awards: EXC 2047: Hausdorff Center for Mathematics (HCM), G4429601001, G8847963564