### 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.

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.

#### Keywords

Random degree; random differential inclusions; random operators; random fixed points; random periodic orbits; transformation to the deterministic case; randomization scheme

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