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Binary statistical experiments with persistent nonlinear regression


Author: D. V. Koroliouk
Translated by: V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 91 (2014).
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
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Abstract | References | Similar Articles | 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.


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  • 1. D. V. Korolyuk, Two-component binary statistical experiments with persistent linear regression, Teor. Ĭmovīr. Mat. Stat. 90 (2014), 91–101 (Ukrainian, with English, Russian and Ukrainian summaries); English transl., Theory Probab. Math. Statist. 90 (2015), 103–114. MR 3242023
  • 2. Stewart N. Ethier and Thomas G. Kurtz, Markov processes, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics, John Wiley & Sons, Inc., New York, 1986. Characterization and convergence. MR 838085
  • 3. A. V. Skorokhod, \cyr Asimptoticheskie metody teorii stokhasticheskikh differentsial′nykh uravneniĭ, “Naukova Dumka”, Kiev, 1987 (Russian). MR 913305
  • 4. Yu. V. Borovskikh and V. S. Korolyuk, Martingale approximation, VSP, Utrecht, 1997. MR 1640099
  • 5. A. N. Shiryaev, Probability-2, MCNMO, Moscow, 2004. (Russian)
  • 6. Albert N. Shiryaev, Essentials of stochastic finance, Advanced Series on Statistical Science & Applied Probability, vol. 3, World Scientific Publishing Co., Inc., River Edge, NJ, 1999. Facts, models, theory; Translated from the Russian manuscript by N. Kruzhilin. MR 1695318
  • 7. Yu. S. Mishura and G. M. Shevchenko, Mathematics of Finance, Kyiv University Publishing House, Kyiv, 2011. (Ukrainian)
  • 8. 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 Methods Appl. Sci. 8 (1998), no. 2, 327–358. MR 1618474, https://doi.org/10.1142/S0218202598000147
  • 9. V. S. Korolyuk and D. Koroliuk, Diffusion approximation of stochastic Markov models with persistent regression, Ukraïn. Mat. Zh. 47 (1995), no. 7, 928–935 (English, with English and Ukrainian summaries); English transl., Ukrainian Math. J. 47 (1995), no. 7, 1065–1073 (1996). MR 1367948, https://doi.org/10.1007/BF01084902

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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

DOI: https://doi.org/10.1090/tpms/967
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