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On Solvability of Stochastic Differential Inclusions With Current Velocities

Applicable Analysis, 2012
An existence of solution theorem is obtained for stochastic differential inclusions given in terms of the so-called current velocities (direct analogues of ordinary velocity of deterministic systems) and quadratic mean derivatives (giving information on the diffusion coefficient) on the flat n-dimensional torus.
Yuri E. Gliklikh, Alla V. Makarova
exaly   +2 more sources

Stochastic Differential Inclusions and Applications

Springer Optimization and Its Applications, 2013
MichaƂ Kisielewicz
exaly   +2 more sources

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
openaire   +1 more source

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.
openaire   +1 more source

On the problem of stochastic differential inclusions

Journal of Soviet Mathematics, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

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
openaire   +2 more sources

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.
openaire   +3 more sources

Stabilization for Stochastic Nonlinear Differential Inclusion Systems with Time Delay

Circuits, Systems, and Signal Processing, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zongcai Jiang   +2 more
openaire   +3 more sources

Lipschitzian quantum stochastic differential inclusions

International Journal of Theoretical Physics, 1992
The author studies quantum stochastic differential inclusions. An existence theorem with a very long proof for the solution of Lipschitzian quantum stochastic differential inclusions is the main result. Relationships between these solutions and those of the convexifications of the inclusions are also studied.
openaire   +1 more source

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   +2 more
openaire   +1 more source

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