| Abstract: |
| Since the pioneering work of Robert Aumann, the notion of set-valued integrals for multivalued functions has attracted the interest of many authors both from theoretical and practical points of view. In particular, the theory has been developed extensively, among others, with applications to optimal control theory, mathematical economics, theory of differential inclusions and set-valued differential equations. Later, the notion of the integral for set-valued functions has been extended to a stochastic case where set-valued Ito and Stratonovich integrals have been studied and applied to stochastic differential inclusions and set-valued stochastic differential equations. On the other hand, in a single-valued case, one can consider stochastic integration with respect to non-semimartingale integrators such as the Mandelbrot fractional Brownian motion which has Holder continuous sample paths. Such integrals can be understood in the sense of Young. This kind of integrals have been developed and widely used in the theory of differential equations by many authors. Thus it seems reasonable to investigate also differential inclusions driven by a fractional Brownian motion and Young type integrals also.
The talk concerns both the properties of set-valued Young integrals and topological properties of solutions of Young differential inclusions. In particular, we present that the set of all solutions is compact in the space of continuous functions. Also its dependence on initial conditions as well as properties of reachable sets of solutions with respect to time will be established. |
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