# On perturbations of ordinary differential equations with non-Lipschitz coefficients by a small-noise

Professor Andrey Pilipenko from the Kiev Polytechnic Institute will give a talk with title "On perturbations of ordinary differential equations with non-Lipschitz coefficients by a small-noise".

Abstract

We study the limit behavior of differential equations with non-Lipschitz coefficients that are perturbed by a small self-similar noise. It is proved that the limiting process is equal to the maximal solution or minimal solution with certain probabilities $$p_+$$ and $$p_+ = 1- p_-$$, respectively. We propose a space-time transformation that reduces the investigation of the original problem to the study of the exact growth rate of a solution to a certain SDE with self-similar noise. This problem is interesting in itself. Moreover, the probabilities $$p_+$$ and $$p_-$$ coincide with probabilities that the solution of the transformed equation converges to $$+\infty$$  or $$-\infty$$  as $$t\to\infty$$, respectively. Multidimensional generalizations are also considered.

Results are based on the joint research with F. N. Proske.

Welcome to the seminar!

## Organizer

Prof. Frank Norbert Proske
Published Oct. 16, 2018 10:42 PM - Last modified Oct. 16, 2018 10:42 PM