Exponential almost sure synchronization of one-dimensional diffusions with nonregular coefficients. Issue 4 (4th July 2021) - Aryasova, Olga; Pilipenko, Andrey; Roelly, Sylvie
Abstract: We study the asymptotic behavior of a real-valued diffusion whose nonregular drift is given as a sum of a dissipative term and a bounded measurable one. We prove that two trajectories of that diffusion converge almost sure to one another at an exponential explicit rate as soon as the dissipative coefficient is large enough. A similar result in Lp is obtained.