2024/01/18 by Łukasz Mądry, Mądry, Łukasz, Paul Gassiat +1
Economics, Econometrics and Finance · Engineering · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Financial Risk and Volatility Modeling #Fluid Dynamics and Turbulent Flows #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2401.09970
openalex publication_date 2024/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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).