Stability Analysis of Stochastic Dynamic Systems under Poisson Perturbations. I. General Analysis of Stability of Solutions of Stochastic Differential Equations under Poisson Perturbations

2005 ◽  
Vol 41 (4) ◽  
pp. 531-540
Author(s):  
I. V. Darijtchuk ◽  
V. K. Jasynsky ◽  
E. V. Jasynsky
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Dynamic Systems ◽  
General Analysis ◽  
Stochastic Dynamic ◽  
Stability Of Solutions ◽  
Analysis Of Stability ◽  
Stochastic Dynamic Systems

scholarly journals Existence and Uniqueness of Solution of Stochastic Dynamic Systems with Markov Switching and Concentration Points

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Taras Lukashiv ◽  
Igor Malyk
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Dynamic Systems ◽  
Existence And Uniqueness ◽  
Markov Switching ◽  
Uniqueness Of Solution ◽  
Stochastic Dynamic ◽  
Uniqueness Of Solutions ◽  
Stochastic Dynamic Systems ◽  
Theoretical Results

In this article the problem of existence and uniqueness of solutions of stochastic differential equations with jumps and concentration points are solved. The theoretical results are illustrated by one example.

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.

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