On perturbation of an ODE with non-Lipschitz coefficients by a small noise & On mutual behavior of solutions of an SDE with non-regular drift

04.02.2019, 10:15  –  Golm, Haus 9, Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Olga Aryasova & Andrey Pilipenko

10:15-11:00 : A. Pilipenko, On pertubertation of an ODE with non-Lipschitz coefficients by a small noise

We study the limit behavior of an ordinary differential equation with non-Lipschitz coefficients that are perturbed by a small noise. Perturbed equations may have unique solutions while the initial ODE does not have a unique solution. Hence a limit of perturbed SDEs may be interpreted as a natural selection of a solution to the initial ODE.

The identification of the limit is closely related with averaging principle and also with a study of the exact growth rate of solutions to SDEs.

11:00-11:45 : O. Aryasova, On mutual behavior of solutions of an SDE with non-regular drift

 We consider a multidimensional stochastic differential equation with a Gaussian noise and a drift vector having a jump discontinuity along a hyperplane. The large time behavior of the distance between two solutions starting from different points is studied. We also prove existence and uniqueness of a strictly stationary solution.