Results 1 to 10 of about 102 (91)

Asynchronous stochastic approximation with differential inclusions [PDF]

Stochastic Systems, 2012
The asymptotic pseudo-trajectory approach to stochastic approximation of Benaïm, Hofbauer and Sorin is extended for asynchronous stochastic approximations with a set-valued mean field.
David S. Leslie, Steven Perkins
doaj   +6 more sources

Stochastic Approximations and Differential Inclusions [PDF]

SIAM Journal on Control and Optimization, 2005
The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benaïm and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications
Sylvain Sorin, Michel Benaïm, Josef Hofbauer   +2 more
exaly   +5 more sources

Null Controllability of Hilfer Fractional Stochastic Differential Inclusions

Fractal and Fractional, 2022
This paper gives the null controllability for nonlocal stochastic differential inclusion with the Hilfer fractional derivative and Clarke subdifferential.
Hamdy M. Ahmed, Mahmoud M. El-Borai, Wagdy El-Sayed, Alaa Elbadrawi   +3 more
doaj   +3 more sources

Stochastic Approximations and Differential Inclusions, Part II: Applications [PDF]

Mathematics of Operations Research, 2006
We apply the theoretical results on “stochastic approximations and differential inclusions” developed in Benaïm et al. [M. Benaïm, J. Hofbauer, S. Sorin. 2005. Stochastic approximations and differential inclusions. SIAM J. Control Optim. 44 328–348] to several adaptive processes used in game theory, including classical and generalized approachability ...
Sylvain Sorin, Michel Benaïm, Josef Hofbauer   +2 more
exaly   +6 more sources

Stochastic Approximation With Discontinuous Dynamics, Differential Inclusions, and Applications

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
Gang George Yin, Nhu Nguyen
exaly   +3 more sources

The Interrelation Between Stochastic Differential Inclusions and Set-Valued Stochastic Differential Equations

Journal of Mathematical Analysis and Applications, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marek T Malinowski, Mariusz Michta
exaly   +3 more sources

Stochastic Differential Inclusions and Diffusion Processes

Journal of Mathematical Analysis and Applications, 2007
The connexion between weak solutions of stochastic differential inclusions and solutions of partial differential inclusions are explored. The results are facilitated by the use of an appropriate continuous approximation selection theorem.
Michał Kisielewicz
exaly   +3 more sources

On Connections Between Stochastic Differential Inclusions and Set-Valued Stochastic Differential Equations Driven by Semimartingales

Journal of Differential Equations, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Michta
exaly   +3 more sources

Trajectory controllability of Clarke subdifferential type Hilfer fractional stochastic differential inclusion with non-instantaneous impulsive effects and deviated argument

Results in Control and Optimization, 2023
This manuscript is devoted to analyse the solvability and trajectory controllability of Hilfer fractional non-instantaneous impulsive stochastic differential inclusion with Clarke subdifferential and deviated argument.
N. Durga, Muslim Malik
doaj   +1 more source

Trajectory Controllability of Clarke Subdifferential-Type Conformable Fractional Stochastic Differential Inclusions with Non-Instantaneous Impulsive Effects and Deviated Arguments

Fractal and Fractional, 2023
In this study, the multivalued fixed point theorem, Clarke subdifferential properties, fractional calculus, and stochastic analysis are used to arrive at the system’s mild solution (1). Furthermore, the mean square moment for the aforementioned system (1)
Dimplekumar Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran   +3 more
doaj   +1 more source