Title | Statistical experiments with persistent linear regression in the Markov random medium |
Publication Type | Journal Article |
Year of Publication | 2015 |
Authors | Koroliouk, DV |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2015.04.012 |
Issue | 4 |
Section | Mathematics |
Pagination | 12-17 |
Date Published | 4/2015 |
Language | Ukrainian |
Abstract | The statistical experiments (SE) with persistent non-linear regression are considered in the discrete-continuous time $k=[Nt]$, $ 0\leq t\leq T$. The directing parameters of the regression function increments depend on the state of an embedded Markov chain in the (homogeneous in time) uniformly ergodic Markov process, which describes the states of the random medium. SE are defined by the solutions of stochastic difference equations with two components: predictive and stochastic (martingale-difference). The obtained approximation in the series scheme with series parameter $N$ (size of the sample), as $N\rightarrow \infty$, is a diffusion Ornstein–Uhlenbeck-type process. The parameters of drift and diffusion are determined by averaging over the stationary distribution of the embedded Markov chain.
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Keywords | linear regression, Markov random medium |
1. Koroliuk D. V. Dopov. Nac. akad. nauk. Ukr., 2014, 3: 18–24 (in Russian).
2. Koroliuk D. V. Dopov. Nac. akad. nauk. Ukr., 2014, 8: 28–34 (in Ukrainian).
3. Borovskikh Yu. V., Korolyuk V. S. Martingale approximation, Utrecht: VSP, 1997.
4. Skorokhod A.V. Asymptotic methods in the theory of stochastic differential equations, Kiev: Nauk. Dumka, 1987 (in Russian).
5. Korolyuk V. S., Limnios N. Stochastic systems in merging phase space, Singapore: World Scientific: 2005. https://doi.org/10.1142/5979
6. Korolyuk V. S., Korolyuk V. V. Stochastic models of systems, Dordrecht: Kluwer, 1999. https://doi.org/10.1007/978-94-011-4625-8
7. Ethier S. N., Kurtz T. G. Markov processes: characterization and convergence, New York: Wiley, 1986. https://doi.org/10.1002/9780470316658
8. Nevelson M. B., Khas’minskii R. Z. Stochastic approximation and recursive estimation, Moscow: Nauka, 1972 (in Russian).