Diffusion approximation of statistical experiments with persistent non-linear regression and equilibrium

TitleDiffusion approximation of statistical experiments with persistent non-linear regression and equilibrium
Publication TypeJournal Article
Year of Publication2014
AuthorsKoroliouk, DV
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2014.08.028
Issue8
SectionMathematics
Pagination28-34
Date Published8/2014
LanguageUkrainian
Abstract

We propose an approximation of statistical experiments with persistent non-linear regression and equilibrium by Markov processes in the discrete-continuous time: k = [Nt], 0 ≤ t ≤ T , for which the diffusion approximation of an Ornstein–Uhlenbeck type process with continuous time is constructed.

Keywordsdiffusion approximation, equilibrium, non-linear regression
References: 

1. Koroliouk D. V. Dopov. Nac. akad. nauk Ukr., 2014, No 3: 18–24 (in Russian).
2. Koroliouk D. V. Ukr. mat. vestn., 2013, 10, No 4: 497–506 (in Russian).
3. Ethier S. N., Kurtz T. G. Markov processes: characterization and convergence, New York: Wiley, 1986. https://doi.org/10.1002/9780470316658
4. Skorokhod A.V. Asymptotic methods in the theory of stochastic differential equations, Kiev: Nauk. Dumka, 1987 (in Russian).
5. Koroliuk V. S., Limnios N. Stochastic systems in merging phase, Singapore; London: Space, World Scientific, 2005. https://doi.org/10.1142/5979
6. Gikhman I. I., Skorokhod A. V. Stochastic differential equations and their applications, Kyiv: Nauk. dumka, 1982 (in Russian).
7. Koroliuk D. V. Teoriia imovirnostei i matem. statystyka, 2014, No 91 (in Ukrainian).