Results 171 to 180 of about 2,483,773 (237)

Stochastic Invariance for Differential Inclusions

Set-Valued and Variational 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 ...
Hélène Frankowska, Jean-Pierre Aubin, Giuseppe Da Prato   +2 more
exaly   +3 more sources

Stochastic Differential Inclusions

Set-Valued Stochastic Integrals and Applications, 2020
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.
M. Kisielewicz
semanticscholar   +4 more sources

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
Michał Kisielewicz
exaly   +2 more sources

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
openaire   +2 more sources

A discussion on approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions

Asian journal of control, 2021
In this paper, the approximate controllability of Sobolev‐type Hilfer neutral fractional stochastic differential inclusions in Hilbert spaces is considered.
C. Dineshkumar, Kottakkaran Sooppy Nisar, R. Udhayakumar, V. Vijayakumar   +3 more
semanticscholar   +1 more source

Weak compactness of weak solutions sets of forward-backward stochastic differential inclusions

Stochastic Analysis and Applications, 2023
The main result of the article deals with weak compactness of weak solutions sets of forward-backward stochastic differential inclusions. The main result is preceded by existence theorem for considered forward-backward stochastic differential inclusions.
M. Kisielewicz
semanticscholar   +1 more source

ON OPTIMAL SOLUTIONS OF STOCHASTIC DIFFERENTIAL INCLUSIONS WITH BACKWARD MEAN DERIVATIVES

Global and Stochastic Analysis, 2023
. For a stochastic differential inclusion given in terms of backward mean derivatives, we prove the existence of optimal solution minimizing a certain cost criterion.
Yuri Gliklikh, A. Grankina
semanticscholar   +1 more source

New discussion about the approximate controllability of fractional stochastic differential inclusions with order 1 < r < 2

Asian journal of control, 2021
In this manuscript, our main focus is about the approximate controllability of fractional stochastic differential inclusions with order 1 
C. Dineshkumar, K. Nisar, R. Udhayakumar, V. Vijayakumar   +3 more
semanticscholar   +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