| Abstract: |
| In the talk we present new types of set-valued integrals which establish a
generalization of a single-valued Young integral. In a single-valued case
the Young integral has been used in a wide range of applications, in
particular, one can consider stochastic integration and stochastic equations
concerning non-semimartingale integrators such as the Mandelbrot
fractional Brownian motion which has Holder continuous sample paths.
Thus it seems reasonable to investigate Young-type integrals for multivalued
functions and their applications to differential inclusions driven by such
new types of integrals. In the presentation, we shall establish properties of
different types of set-valued Young integrals for classes of set-valued
functions being Holder continuous or with bounded p-variations. These
properties are crucial in the studies of different types of Young
differential inclusions.
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References
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1. M. Michta, J. Motyl, Selection properties and set-valued Young integrals
of set-valued functions, Results Math. 75, 164 (2020).
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2. M. Michta, J. Motyl, Set-valued functions of bounded generalized
variation and set-valued Young integrals, J. Theor. Probab. 35 (2022),
528-549.
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3. M. Michta, J. Motyl, Solution sets for Young differential inclusions,
Qual. Theory Dyn. Syst. 22, 132 (2023).
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4. M. Michta, J. Motyl, Properties of set-valued Young integrals and Young
differential inclusions generated by sets of Holder functions, Nonlinear
Differ. Equ. Appl. 31, article no 70 (2024). |
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