Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are
pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics …

Differential equations that switch between different modes of behavior across a surface of
discontinuity are used to model, for example, electronic switches, mechanical contact …

In this article we develop a new approach to construct solutions of stochastic equations with
merely measurable drift coefficients. We aim at demonstrating the principles of our technique …

1. Differential equations with random right-hand sides and impulsive effects. 1.1. An
impulsive process as a solution of an impulsive system. 1.2. Dissipativity. 1.3. Stability and …

The zero-noise result for Peano phenomena of Bafico and Baldi (1982) is revisited. The
original proof was based on explicit solutions to the elliptic equations for probabilities of exit …

We give a brief introduction and overview of the topic of regularization and well-posedness
by noise for ordinary and partial differential equations. The article is an attempt to outline in a …

The problem on identification of a limit of an ordinary differential equation with discontinuous
drift that perturbed by a zero-noise is considered in multidimensional case. This problem is a …

Sliding motion is evolution on a switching manifold of a discontinuous, piecewise-smooth
system of ordinary differential equations. In this paper we quantitatively study the effects of …

Electron. Commun. Probab. 18 (2013), no. 31, DOI: 10.1214/ECP.v18-2587 Page 1 Electron.
Commun. Probab. 18 (2013), no. 31, 1–7. DOI: 10.1214/ECP.v18-2587 ISSN: 1083-589X …

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 …