Random topological degree and random differential inclusions

Abstract

We present a random topological degree effectively applicable mainly to periodic problems for random differential inclusions. These problems can be transformed to the existence problems of random fixed points or periodic orbits of the associated Poincaré translation operators. The solvability can be so guaranteed either directly by means of nontrivial topological invariants (random degree, index of a random direct potential) or via a randomization scheme using deterministic results which are ``periodicity stable'' under implemented parameter values.