| Abstract: |
| In the talk, we present new types of differential inclusions with a
set-valued Young integral, which generalize a single-valued Young
differential equation. In the single-valued case, the Young integral has
been used in a wide range of applications. In particular, one can consider
stochastic equations with respect to non-semimartingale integrators, such as
the Mandelbrot fractional Brownian motion, which has H\{o}lder continuous
sample paths. Thus, it seems reasonable to investigate differential
inclusions driven by such a new type of integral. In the presentation, we
shall establish the main properties of solution sets of Young differential
inclusions. In particular, solutions to an abstract optimization problem
related to the inclusion will be presented.
References:
1. M. Michta, J. Motyl, Selection properties and set-valued Young integrals
of set-valued functions, Results Math. 75, 164 (2020).
2. M. Michta, J. Motyl, Set-valued functions of bounded generalized
variation and set-valued Young integrals, J. Theor. Probab. 35 (2022),
528-549.
3. M. Michta, J. Motyl, Solution sets for Young differential inclusions,
Qual. Theory Dyn. Syst. 22, 132 (2023).
4. M. Michta, J. Motyl, Properties of set-valued Young integrals and Young
differential inclusions generated by sets of H\{o}lder functions, Nonliner
Differ. Equ. Appl. 31, article no 70 (2024). |
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