Diffusion approximation of statistical experiments with persistent linear regression and equilibrium

Authors

  • D.V. Koroliouk

DOI:

https://doi.org/10.15407/dopovidi2014.03.018

Keywords:

diffusion approximation, equilibrium, regression, statistical experiments

Abstract

We propose an approximation of statistical experiments with persistent 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.

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References

Koroliuk D. V. Ukr. mat. vestn., 2012, 9, No. 4: 560–567 (in Russian).

Koroliuk D. V. Ukr. mat. vestn., 2013, 10, No. 4: 497-506 (in Russian).

Ethier S. N., Kurtz T. G. Markov processes: characterization and convergence. New York: Wiley, 1986. https://doi.org/10.1002/9780470316658

Skorokhod A.V. Asymptotic methods in the theory of stochastic differential equations, Kiev: Nauk. Dumka, 1987 (in Russian).

Koroliuk V. S., Limnios N. Stochastic systems in merging phase space. Singapore; London: World Scientific, 2005. https://doi.org/10.1142/5979

Gikhman I. I., Skorokhod A. V. Stochastic differential equations and their applications, Kyiv: Nauk. dumka, 1982 (in Russian).

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Published

11.02.2025

How to Cite

Koroliouk, D. (2025). Diffusion approximation of statistical experiments with persistent linear regression and equilibrium . Reports of the National Academy of Sciences of Ukraine, (3), 18–24. https://doi.org/10.15407/dopovidi2014.03.018

Issue

No. 3 (2014): Reports of the National Academy of Sciences of Ukraine

Section

Mathematics

License

Copyright (c) 2025 Reports of the National Academy of Sciences of Ukraine

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