Year: 2024
Type: preprint
Abstract: We consider scalar ODE with a power singularity at the origin, regularized by an additive fractional noise. We show that, as the intensity in front of the noise goes to $0$, the solution converges to the extremal solutions to the ODE (which exit the origin instantly), and we quantify this convergence with subexponential probability estimates. This extends classical results of Bafico and Baldi in the Brownian case. The main difficulty lies in the absence of the Markov property for the system. Our methods combine a dynamical approach due to Delarue and Flandoli, with techniques from the large time analysis of fractional SDE (due in particular to Panloup and Richard).
Authors: Mądry, Łukasz, Gassiat, Paul
Institution: Centre de Recherche en Mathématiques de la Décision
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4391047099