ПРОЦЕДУРА СТОХАСТИЧНОЇ АПРОКСИМАЦІЇ З ІМПУЛЬСНИМ МАРКОВСЬКИХ ЗБУРЕННЯХ

Автор(и)

  • Ярослав Михайлович Чабанюк Національний університет “Львівська політехніка”, м. Львів, Україна
  • Сергей Анатолійович Семенюк Національний університет “Львівська політехніка”, м. Львів, Україна

DOI:

https://doi.org/10.32626/2308-5878.2011-5.244-252

Ключові слова:

stochastic approximation procedure, Markov process, impulsive perturbation.

Анотація

In this paper we discuss asymptotic behavior of the stochastic approximation procedure in case when the regression function is perturbed by the Markov impulsive process. Also we consider the stochastic approximation procedure stability conditions in the terms of existence of Lyapunov's function for the averaged evolution system.

Посилання

Chabanyuk Ya. M. Diffusion process approximation in the averaging schema / Ya. M. Chabanyuk // Papers of NAS of Ukraine. — 2004. — № 12. — P. 35—40.

Nevelson M. B. Stochastic approximation and recurrent estimation / M. B. Nevelson, R. Z. Khasminskii. — M. : Nauka, 1972.

Van Trees H. L. Detection, estimation and modulation theory / H. L. Van Trees // J. Wiley and sons. — N. Y, 1968.

Korolyuk V. S. Stochastic Systems in Merging Phase Space / V. S. Korolyuk, N. Limnius // World Scientific. — 2005.

Korolyuk V. S. Stochastic Models of Systems / V. S. Korolyuk, V. V. Korolyuk. — Kluwer : Dordrecht, 1999.

Chabanyuk Ya. M. Continuous stochastic approximation procedure with singular perturbation under the balance conditions / Ya. M. Chabanyuk // Cybernetics and system analysis. — 2006. — № 3. — P. 1—7.

Ljung L. Stochastic Approximation and Optimization of Random Systems / L. Ljung, G. Pflug, H. Walk. — Basel ; Boston ; Berlin : Birkhauser Verlag, 1992.

Semenyuk S. A. Fluctuations of the stochastic approximation procedure with diffusion perturbations / S. A. Semenyuk // Cybernetics and system analysis. — 2009. — № 5. — P. 176—180.

Semenyuk S. A. Fluctuations of the evolution system with Markov impulsive perturbations / S. A. Semenyuk, Ya. M. Chabanyuk // Matematychni Studii. — 2009. — Vol. 32, № 2. — P. 198—204.

Kiefer E. Stochastic estimation of the maximum of a regression function / E. Kiefer, J. Wolfowitz // Ann. Math. Statist. — 1952. — Vol. 23, № 3. — P. 462—466.

Ruppert D. Almost sure approximations to the Robbins-Monro and Kiefer Wolfowitz processes with dependent noise / D. Ruppert // Ann. Probab. — 1982. — № 10. — P. 178—187.

##submission.downloads##

Опубліковано

2011-04-23

Номер

2011: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 5

Розділ

Статті

Ліцензія

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).