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Weak solutions of stochastic differential Inclusions and their compactness [PDF]

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2009
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known
Michta, Mariusz
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Stochastic Invariance for Differential Inclusions

Set-Valued Analysis, 2000
The first objective of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a stochastic uncertainty driven by a Wiener process and a contingent uncertainty driven by a set-valued map. The second point consists to extend to stochastic differential inclusions the invariance theorem for nonstochastic ...
Aubin, Jean-Pierre, da Prato, Giuseppe, Frankowska, Hélène   +2 more
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Controllability for neutral stochastic functional differential inclusions with infinite delay in abstract space [PDF]

Journal of Mathematical Analysis and Applications, 2006
In this paper, sufficient conditions are given for the controllability of a class of partial stochastic functional differential inclusions with infinite delay in an abstract space with the help of the Leray Schauder nonlinear alternative.
P Balasubramaniam, S K Ntouyas
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Stochastic differential inclusions with Hilfer fractional derivative

Annals of the University of Craiova, Mathematics and Computer Science Series, 2022
In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Meryem Chaouche, Toufik Guendouzi
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Stochastic differential inclusions of Langevin type on Riemannian manifolds

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2001
A set-valued analogue of the classical Langevin equation on a Riemannian manifold is introduced and several existence theorems of inclusions of Langevin type are proved. Let \(v:I\to T_{m_0}M\) be a continuous curve, \({ \mathcal S}v\) the unique \(C^1\)-curve \(\gamma: I\to M\) such that \(\gamma(0) =m_0\) and \(\dot\gamma (t)\) is parallel to the ...
Gliklikh, Yuri E., Obukhovskij, V.
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On the problem of stochastic differential inclusions

Journal of Soviet Mathematics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stochastic Approximations with Constant Step Size and Differential Inclusions

SIAM Journal on Control and Optimization, 2013
We consider stochastic approximation processes with constant step size whose associated deterministic system is an upper semicontinuous differential inclusion. We prove that over any finite time span, the sample paths of the stochastic process are closely approximated by a solution of the differential inclusion with high probability.
Gregory Roth, William H. Sandholm
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Stochastic Differential Inclusions

2013
A stochastic differential inclusion is formulated in terms of stochastic differentials of continuous semimartingales. In particular, concepts of strong and weak solutions of the inclusion \[ dx_t\in F(t,x_t)dt+G(t,x_t)dw_t \] are introduced. Here \(F,G:[0,1]\times R^n\to \text{Comp} (R^n)\) are Borel measurable set-valued mappings.
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Stabilization for Stochastic Nonlinear Differential Inclusion Systems with Time Delay

Circuits, Systems, and Signal Processing, 2016
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Zongcai Jiang, Jinjin Liu, Lili Zhang 0008   +2 more
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Existence results on impulsive stochastic semilinear differential inclusions

International Journal of Dynamical Systems and Differential Equations, 2021
Summary: In this paper, we present some existence results of mild solutions and study the topological structure of solution sets for the following first-order impulsive stochastic semilinear differential inclusions driven by Poisson jumps with periodic boundary conditions. We consider the cases in which the right hand side can be either convex.
Meghnafi, Mustapha, Hammami, Mohamed Ali, Blouhi, Tayeb   +2 more
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