Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach

Королюк, В. С.; Limnios, Nikolaos; Самойленко, И. В.

doi:10.1016/j.crma.2016.04.008

Cited by 10 publications

(8 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is important that the asymptotic behavior of the limit process is concluded with the help of the analysis of parameters of the pre-limit system. This work continues the direction of research carried out in papers [4], [6]- [8], in which the asymptotic properties of evolution models were obtained under conditions of non-classical approximation schemes.…”

supporting

confidence: 65%

See 1 more Smart Citation

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Chabanyuk¹,

Nikitin²,

Хімка³

2019

View full text Add to dashboard Cite

properties of the impulse perturbation process under Levy approximation conditions with the point of equilibrium of the quality criterion, Mat. Stud. 52 (2019), 96-104. For the system of stochastic differential equations with Markov switchings and impulse disturbance in the conditions of Levy approximation of a single equilibrium point of the quality criterion, limiting generators of the impulse process and dynamical system are constructed. In particular, we discuss how the behavior of the boundary process depends on the pre-limiting normalization of the stochastic evolutionary system in the ergodic Markov environment.

show abstract

supporting

confidence: 65%

“…Lemma 3. Under balance condition (4), the solution of the singular perturbation problem for truncated operator is realized by the relation…”

Section: Lemma 2 Generator Of Three Component Markov Processmentioning

confidence: 99%

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Chabanyuk¹,

Nikitin²,

Хімка³

2019

View full text Add to dashboard Cite

show abstract

“…Weak convergence of process (y ε (t), u ε (t), η ε (t)) ⇒ (ŷ(t),û(t),η(t)), ε → 0, follows from convergence of the corresponding generators under condition of compactness of pre-limited set of processes (y ε (t), u ε (t))). In particular, the corresponding theorems on the compactness of processes with independent increments in Levy approximation scheme have been proved in [4].…”

Section: Corollarymentioning

confidence: 99%

“…Analyzing the state of the art concerning asymptotic properties of stochastic evolution models reveals that a complete theory is still to be worked out. Well understood are the models which are given by stochastic differential equations with Markov switchings and impulse or continuous-type perturbations in the classical schemes of averaging or diffusion approximation ([2]- [4]). Also, the asymptotic behavior was investigated of impulse processes with Markov switchings under the conditions of Levy approximation ( [1], [8]- [11]).…”

mentioning

confidence: 99%

Control problem for the impulse process under stochastic optimization procedure and Levy conditions

2021

View full text Add to dashboard Cite

A stochastic approximation procedure and a limit generator of the original problem are constructed for a system of stochastic differential equations with Markov switching and impulse perturbation under Levy approximation conditions with control, which is determined by the condition for the extremum of the quality criterion function.The control problem using the stochastic optimization procedure is a generalization of the control problem with the stochastic approximation procedure, which was studied in previous works of the authors. This generalization is not simple and requires non-trivial approaches to solving the problem. In particular we discuss how the behavior of the boundary process depends on the prelimiting stochastic evolutionary system in the ergodic Markov environment. The main assumption is the condition for uniform ergodicity of the Markov switching process, that is, the existence of a stationary distribution for the switching process over large time intervals. This allows one to construct explicit algorithms for the analysis of the asymptotic behavior of a controlled process. An important property of the generator of the Markov switching process is that the space in which it is defined splits into the direct sum of its zero-subspace and a subspace of values, followed by the introduction of a projector that acts on the subspace of zeros.For the first time, a model of the control problem for the diffusion transfer process using the stochastic optimization procedure for control problem is proposed. A singular expansion in the small parameter of the generator of the three-component Markov process is obtained, and the problem of a singular perturbation with the representation of the limiting generator of this process is solved.

show abstract

“…is uniformly ergodic Markov process in a standart pgase space , is defined by the generator [1], [2], [6], [13] on the Banach space B(X) of real-valued bounded functions with the supremum norm…”

Section: Information Warfare Model With Impulsive Influencementioning

confidence: 99%

Construction Features and Analisis of Warfar Information Model with Markov Switchings under Levy Approximation Conditions

Samoilenko¹,

Nikitin²

2020

Challenges to National Defence in Contemporary Geopolitical Situation

View full text Add to dashboard Cite

We construct and study a continuous model that describes the conflict interaction of two complex systems with non-trivial internal structures. External conflict interaction is modeled by the additional influence of chance. The dynamics of internal conflict are similar to the Lotka-Volterra model, namely the model of information warfare. We interpret the new model of information warfare as the influence of rare events that rapidly change certain ideas of a large number of people. As a result, the number of supporters of different ideas make stochastic jumps that we can see using the Levy approximation scheme. We suggest that such a model could be more natural, as important news now has a quick and wonderful impact on audiences through television and the Internet.

show abstract

Lévy and Poisson approximations of switched stochastic systems by a semimartingale approach

Cited by 10 publications

References 6 publications

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Asymptotic properties of the impulse perturbation process under Levy approximation conditions

Control problem for the impulse process under stochastic optimization procedure and Levy conditions

Construction Features and Analisis of Warfar Information Model with Markov Switchings under Levy Approximation Conditions

Contact Info

Product

Resources

About