Stochastic representation of partial differential inclusions [PDF]
Journal of Mathematical Analysis and Applications, 2009 Partial differential inclusions of the form \(u_t^\prime \in \mathbb L _{FG}u+cu\) and \(\psi \in \mathbb L_{FG}u+cu\), where \(\mathbb L_{FG}\) is a uniformly parabolic second order set-valued operator, are considered. In particular, based on diffusions properties of weak solutions to stochastic differential inclusions, some existence and ...
Michał Kisielewicz +1 more
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Stochastic Langevin Differential Inclusions with Applications to Machine Learning [PDF]
CoRR, 2022 Stochastic differential equations of Langevin-diffusion form have received significant attention, thanks to their foundational role in both Bayesian sampling algorithms and optimization in machine learning. In the latter, they serve as a conceptual model of the stochastic gradient flow in training over-parameterized models.
Fabio V. Difonzo +2 more
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Some optimal control problems for partial differential inclusions [PDF]
Opuscula Mathematica, 2008 Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.
Michał Kisielewicz
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Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions [PDF]
International Journal of Stochastic Analysis, 2011 We discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one.
A. Vinodkumar, A. Boucherif
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On the Relationship Between Solutions of Stochastic and Random Differential Inclusions [PDF]
Stochastic Analysis and Applications, 2003 Some results on the relationship of the solutions of a stochastic di erential inclusion and the corresponding random di erential inclusion obtained after a change of variable are proved. As a consequence, we obtain the pullback convergence of the solutions of the stochastic inclusion to a compact random set.
Caraballo Garrido, Tomás +2 more
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Approximate Controllability of Hilfer Fractional Stochastic Evolution Inclusions of Order 1 < q < 2 [PDF]
Fractal and FractionalThis paper addresses the approximate controllability results for Hilfer fractional stochastic differential inclusions of order ...
Anurag Shukla +4 more
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The effects of Clarke sub-differential and Poisson jumps on nonlocal controllability of Sobolev-type fractional stochastic differential inclusions [PDF]
Journal of Inequalities and ApplicationsThis paper explores Sobolev-type Atangana–Baleanu fractional stochastic differential inclusions driven by fractional Brownian motion, incorporating Clarke sub-differentials, Poisson jumps, and nonlocal conditions.
Wael W. Mohammed +4 more
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Finite dimensional stochastic differential inclusions [PDF]
, 2008 This paper offers an existence result for finite dimensional stochastic differential inclusions with maximal monotone drift and diffusion terms. Kravets studied only set-valued drifts in [5], whereas Motyl [4] additionally observed set-valued diffusions in an infinite dimensional context.
Bauwe, Anne, Grecksch, Wilfried
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Aumann Type Set-valued Lebesgue Integral and Representation Theorem [PDF]
International Journal of Computational Intelligence Systems, 2009 n this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact ...
Jungang Li, Shoumei Li
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Stochastic approximation with discontinuous dynamics, differential inclusions, and applications
The Annals of Applied Probability, 2023 This work develops new results for stochastic approximation algorithms. The emphases are on treating algorithms and limits with discontinuities. The main ingredients include the use of differential inclusions, set-valued analysis, and non-smooth analysis, and stochastic differential inclusions. Under broad conditions, it is shown that a suitably scaled
Nguyen, Nhu, Yin, George
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