12. Juni 2019
Ilya Pavlyukevich (Friedrich Schiller University Jena)
Small noise behavior of Levy-driven Langevin equations
Abstract:
We consider a second-order Langevin equation for the motion of a particle subject to a non-linear friction force being a power of the particle's velocity, $F=-|v|^\beta \sign(v)$, $\beta\in\mathbb R$, and random Levy-perturbations, and determine the law of the displacement process in the limit of the small noise amplitude. This a joint work with Alexei Kulik, Wroclaw.
Andrei Pilipenko (Ukrainian National Academy of Sciences and Kiev Polytechnic Institute)
On a selection problem for small noise perturbation of unstable
dynamical systems
Abstract:
We study a 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, if perturbed SDEs converge when an intensity of the noise tend to zero, then their limit may be interpreted as a natural selection of a solution to the initial ODE.