Random fixed points and viable random solutions of functional- differential inclusions (Q1823546)

The author studies random functional-differential inclusions in Banach spaces and looks for viable solutions which depend measurably on a random parameter. He proposes a general scheme which allows us to neglect the randomness: If for each value of the parameter the corresponding deterministic problem has a solution, and some measurability assumptions are satisfied, then there exists a random solution. Both classical and absolutely continuous solutions are treated. As an auxiliary result, the author proves a general random fixed point theorem for multivalued mappings. Measurable and continuous selection theorems play the key role in the proofs.