DIRaH - Differential Inclusions with Randomness and Hysteresis

Overview of DIRaH project

The project is aimed at developing analytical and topological methods for studying problems described in terms of differential equations and measure differential inclusions with stochastic perturbations, for example directed by fractional Brownian motion, and differential equations or inclusions with fractional derivatives. We will also develop numerical schemes as well as parametric and nonparametric methods of statistical estimation for these problems.

We will focus on differential inclusions with randomness in connection with problems with hysteresis. Such problems include differential inclusions with monotone operators, in particular different forms of the sweeping process and Skorokhod reflection problem. Applications to elastoplastic systems with springs will be a special topic of interest.

Support: DIRaH is a french-russian project which began in 2020 and is supported by both CNRS and RFBR.