Exponential a.s. synchronization of one-dimensional diffusions with non-regular coefficients

Autoren: Olga Aryasova, Andrey Pilipenko, Sylvie Roelly (2020)

 We study the asymptotic behaviour of a real-valued diffusion whose non-
regular drift is given as a sum of a dissipative term and a bounded measurable one.
We prove that two trajectories of that diffusion converge a.s. to one another at an
exponential explicit rate as soon as the dissipative coefficient is large enough. A
similar result in Lp is obtained.

Stochastic Analysis and Applications

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