Binary statistical experiments with persistent nonlinear regression
Author:
D. V. Koroliouk
Translated by:
V. Semenov
Journal:
Theor. Probability and Math. Statist. 91 (2015), 71-80
MSC (2010):
Primary 62F05, 60J70, 62M05
DOI:
https://doi.org/10.1090/tpms/967
Published electronically:
February 3, 2016
MathSciNet review:
3364124
Full-text PDF Free Access
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Additional Information
Abstract: A sequence of binary stochastic experiments with persistent nonlinear regression is considered. The regression is defined as a product of a linear directed force and nonlinear term changing the directed force in a neighborhood of boundary points. A stochastic approximation for the sequence of stationary experiments is constructed with the help of an autoregressive process with normal perturbation. A stochastic approximation of the sequence of exponential stochastic experiments is also constructed with the help of an exponential autoregressive process.
References
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- Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Publishing House, Kyiv, 2011. (Ukrainian)
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References
- D. V. Koroliouk, Two component binary statistical experiments with persistent linear regression, Teor. Imovirnost. Math. Statist. 90 (2014), 91–101; English transl. in Theor. Probability and Math. Statist. 90 (2015), 103–114. MR 3242023
- S. N. Ethier and T. G. Kurtz, Markov Processes: Characterization and Convergence, Wiley, New York, 1986. MR 838085 (88a:60130)
- A. V. Skorokhod, Asymptotic Methods in the Theory of Stochastic Differential Equations, “Naukova dumka”, Kiev, 1987; English transl., American Mathematical Society, Providence, RI, 2009. MR 913305 (88m:60164)
- Yu. V. Borovskikh and V. S. Korolyuk, Martingale Approximation, VSP, 1997. MR 1640099 (99f:60001)
- A. N. Shiryaev, Probability–2, MCNMO, Moscow, 2004. (Russian)
- A. N. Shiryaev, Essentials of Stochastic Finance: Facts, Models, Theory “Fazis”, Moscow, 1998; English transl., World Scientific Pub. Co. Inc., Singapore, 1999. MR 1695318 (2000e:91085)
- Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Publishing House, Kyiv, 2011. (Ukrainian)
- M. Abundo, L. Accardi, L. Stella, and N. Rosato, A stochastic model for the cooperative relaxation of proteins, based on a hierarchy of interactions between amino acidic residues, Math. Models and Methods in Appl. Sciences (1998) no. 8, 327–358. MR 1618474 (99g:92020)
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Additional Information
D. V. Koroliouk
Affiliation:
Institute of Telecommunications and Global Information Space of National Academy of Science of Ukraine, Chokolovskiĭ Blvd., 13, Kyiv, 03110, Ukraine
Email:
dimitri.koroliouk@ukr.net
Keywords:
Binary statistical experiment,
persistent regression,
equilibrium state,
stochastic approximation,
exponential stochastic experiment,
exponential normal autoregressive process
Received by editor(s):
April 26, 2013
Published electronically:
February 3, 2016
Article copyright:
© Copyright 2016
American Mathematical Society
