scholarly journals Some causal connections between stochastic dynamic systems

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 865-873
Author(s):  
Ljiljana Petrovic
Keyword(s):  
Dynamic System ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Stochastic Dynamic ◽  
Realization Problem ◽  
Stochastic Dynamic System ◽  
Causal Connections ◽  
Causality Relationship ◽  
Stochastic Dynamic Systems

In this paper we consider a problem that follows directly from realization problem: how to find Markovian representations , even minimall, for a given family of Hilbert spaces, understood as outputs of a stochastic dynamic system S1, provided it is in a certain causality relationship with another family of Hilbert spaces , i. e. with some informations about states of a stochastic dynamic system S2. This paper is continuation of the papers Gill and Petrovic [7] and Petrovic [16,17].

scholarly journals Optimal Control of Stochastic Dynamic Systems of a Random Structure with Poisson Switches and Markov Switching

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Svitlana V. Antonyuk ◽  
Marian F. Byrka ◽  
Mykola Y. Gorbatenko ◽  
Taras O. Lukashiv ◽  
Igor V. Malyk
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Optimal Control ◽  
Dynamic System ◽  
Dynamic Systems ◽  
Markov Switching ◽  
Stochastic Dynamic ◽  
Random Structure ◽  
Stochastic Dynamic System ◽  
Stochastic Dynamic Systems

The problem of synthesis of the optimal control for a stochastic dynamic system of a random structure with Poisson perturbations and Markov switching is solved. To determine the corresponding functions for Bellman functional and optimal control the system of ordinary differential equation is investigated.

scholarly journals One Form of Lyapunov Operator for Stochastic Dynamic System with Markov Parameters

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Taras Lukashiv
Keyword(s):  
Dynamic System ◽  
Dynamic Systems ◽  
Stochastic Dynamic ◽  
Random Structure ◽  
Constant Delay ◽  
Infinitesimal Operator ◽  
Markov Parameters ◽  
Stochastic Dynamic System ◽  
Lyapunov Operator ◽  
Stochastic Dynamic Systems

The form of weak infinitesimal operator of Lyapunov type on solutions of stochastic dynamic systems of random structure with constant delay which exist under the action of Markov perturbations is obtained.

scholarly journals Approximate Controllability of Sobolev Type Nonlocal Fractional Stochastic Dynamic Systems in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Mourad Kerboua ◽  
Amar Debbouche ◽  
Dumitru Baleanu
Keyword(s):  
Control Systems ◽  
Hilbert Spaces ◽  
Dynamic Systems ◽  
Approximate Controllability ◽  
Dynamic Control ◽  
Sufficient Conditions ◽  
Sobolev Type ◽  
Stochastic Dynamic ◽  
Deterministic Control ◽  
Stochastic Dynamic Systems

We study a class of fractional stochastic dynamic control systems of Sobolev type in Hilbert spaces. We use fixed point technique, fractional calculus, stochastic analysis, and methods adopted directly from deterministic control problems for the main results. A new set of sufficient conditions for approximate controllability is formulated and proved. An example is also given to provide the obtained theory.

scholarly journals Markovian extensions and reductions of a family ofσ-algebras

1984 ◽  
Vol 7 (3) ◽  
pp. 523-528 ◽  
Author(s):  
Jelena Bulatovic Gill
Keyword(s):  
Dynamic System ◽  
The Other ◽  
Stochastic Dynamic ◽  
Realization Problem ◽  
Stochastic Dynamic System ◽  
Flow Of Information

In the first part of this paper different properties of two special realizations of a stochastic dynamic system, as well as relationships between the realization problem and a problem derived from it are investigated. In the second part, solutions of the following two problems (that follow directly from the realization problem) are given: how to find the minimal (resp. maximal) markovlan flow of information (understood as a family ofσ-algebras) that contains (resp. is contained in) given output of a system, and is such that each of these two flows of information is equally predictable by the other one.

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