Opšti tip stabilnosti stohastičkih funkcionalnih diferencijalnih jednačina
General decay stability of stochastic functional differential equations
Докторанд
Pavlović-Rajković, Gorica A.Ментор
Janković, SvetlanaЧланови комисије
Petrović, LjiljanaJovanović, Miljana
Milošević, Marija
Метаподаци
Приказ свих података о дисертацијиСажетак
In this thesis, pth moment and almost sure stability on a general decay rate for
several types of stochastic functional differential equations were studied. By applying
Razumikhin method and Lyapunov method stability criteria were obtained.
Having in mind that some types of stochastic differential equations are not exponentially
stable, the information about the stability with respect to a certain lower
decay rate is very important, which was the motive for research in this paper.
Some future research could focus on application of Krasovskii-Lyapunov method
for exploring the general decay stability of the already studied types of stochastic
differential equations. In this way, we could get different stability and decay rate
criteria with respect to those obtained in the thesis.
The research based on the modified results of this thesis could be continued for
studying stability of various classes of stochastic functional differential equations
with respect to martingale and martingale me...asures.
The research on pth moment and almost sure stability and pth moment instability
on a general decay rate for stochastic functional differential equations with
Markovian switching and delayed impulses could be extended to stochastic differential
equations with random impulses and Markovian switching which more
realistically describe processes impulsive in kind. Also, Razumikhin method and
Lyapunov method could be applied in studying pth moment and almost sure stability
on a general decay rate for hybrid impulsive stochastic differential equations
with switching not defined by Markov chain law as well as stochastic neural networks.
Moreover, these methods could be used for studying general decay stability
of all the above mentioned types of impulsive stochastic differential equations with
respect to martingale and martingale measures.
Some future research could be based on the application of LMI theory results to
studying pth moment and almost sure stability on a general decay rate of perturbed
impulsive stochastic functional differential equations with Markovian switching and
hybrid perturbed impulsive stochastic functional differential equations.