Holomozyi V. Ergodicity and stability of almost homogeneous Markov chains

Українська версія

Thesis for the degree of Doctor of Science (DSc)

State registration number

0524U000059

Applicant for

Specialization

  • 01.01.05 - Теорія ймовірностей і математична статистика

12-03-2024

Specialized Academic Board

Д 26.001.18

Taras Shevchenko National University of Kyiv

Essay

The thesis is devoted to the investigation of the stability of homogeneous and inhomogeneous Markov chains using the coupling method. In this work, the known geometric drift condition was generalized to the inhomogeneous case, and stability estimates for n-steps transition probabilities have been built. In addition, the conditions for geometric ergodicity and stability for the inhomogeneous autoregressive model were obtained. The work also includes estimates for the risk function in the time-inhomogeneous Cramer-Lundberg model. Keywords: Markov chain, ergodicity, staibility, coupling.

Research papers

Golomoziy, V. On geometric recurrence for time-inhomogeneous autoregression // Modern Stochastics: Theory and Applications. 2023. Vol 10, no. 3. P. 1-29.

Golomoziy, V. Exponential moments of simultaneous hitting time for non-atomic Markov chains // Glasnik Matematicki. 2022. Vol 57, iss. 1. P. 129-147.

Golomoziy, V. and Mishura, Y. Stability Estimates for Finite-Dimensional Distributions of Time-Inhomogeneous Markov Chains // Mathematics. 2020. Vol. 8, iss. 2.

Golomoziy, V. Stability of functionals of perturbed Markov chains under the condition of uniform minorization // Random Operators and Stochastic Equations. 2020. Vol. 28, iss. 4. P. 237-251.

Golomoziy, V. Estimates of stability of transition probabilities for non-homogeneous Markov chains in the case of the uniform minorization // Theory of Probability and Mathematical Statistics. 2020. Vol 101. P. 85-101.

Golomoziy, V. On estimation of expectation of simultaneous renewal time of time-inhomogeneous Markov chains using dominating sequence // Modern Stochastics: Theory and Applications. 2019. Vol 6, no. 3. P. 334-343.

Golomoziy, V. and Kartashov, M. Some inequalities for the risk function in the time and space nonhomogeneous Cramer–Lundberg risk model // Theory of Probability and Mathematical Statistics. 2019. Vol 98. P. 243-254.

Golomoziy, V. Properties of the stochastic ordering for discrete distributions and their applications to the renewal sequence generated by a nonhomogeneous Markov chain // Theory of Probability and Mathematical Statistics. 2018. Vol 97. P. 33-43.

Golomoziy, V. An estimate of the expectation of the excess of a renewal sequence generated by a time-inhomogeneous Markov chain if a square-integrable majorizing sequence exists // Theory of Probability and Mathematical Statistics. 2017. Vol 94. P. 53-62.

Golomoziy, V. An estimate for an expectation of the simultaneous renewal for time-inhomogeneous Markov chains // Modern Stochastics: Theory and Applications. 2016. Vol 3, no. 4. P.315-323.

Golomoziy, V. and Kartashov, M. Maximal coupling and V-stability of discrete nonhomogeneous Markov chains // Theory of Probability and Mathematical Statistics. 2016. Vol 93. P. 19-31.

Golomoziy, V. and Kartashov, M. and Kartashov, Y. Impact of the stress factor on the price of widow’s pensions. Proofs // Theory of Probability and Mathematical Statistics. 2016. Vol 92. P. 17-22.

Golomoziy, V. An inequality for the coupling moment in the case of two inhomogeneous Markov chains // Theory of Probability and Mathematical Statistics. 2015. Vol 90. P. 43-56.

Golomoziy, V. and Kartashov, M. Maximal coupling and stability of discrete non-homogeneous Markov chains // Theory of Probability and Mathematical Statistics. 2015. Vol 91. P. 17-27.

Golomoziy, V. and Kartashov, M. On the integrability of the coupling moment for time-inhomogeneous Markov chains // Theory of Probability and Mathematical Statistics. 2014. Vol 89. P. 1-12.

Golomoziy, V. and Kartashov, M. Maximal coupling procedure and stability of discrete Markov chains. I // Theory of Probability and Mathematical Statistics. 2013. Vol 86. P. 93-104.

Golomoziy, V. and Kartashov, M. Maximal coupling procedure and stability of discrete Markov chains. II // Theory of Probability and Mathematical Statistics. 2013. Vol 87. P. 65-68.

Голомозий, В. Оцiнка експоненцiйного моменту для часу одночасного вiдновлення двох випадкових блукань на пiвпрямiй // Вiсник Київського унiверситету. Серiя фiзико-математичнi науки. 2021. Вип. 2. P. 26-31.

Golomoziy, V. Computable Bounds of Exponential Moments of Simultaneous Hitting Time for Two Time-Inhomogeneous Atomic Markov Chains // In: Malyarenko, A., Ni, Y., Rancic, M., Silvestrov, S. (eds) Stochastic Processes, Statistical Methods, and Engineering Mathematics . SPAS 2019. Springer Proceedings in Mathematics and Statistics. Vol 408, 2023. P. 97-119.

Golomoziy, V. and Kartashov, M. and Kartashov, Y. Impact of the stress factor on the price of widow’s pensions. // In: Silvestrov, D., Martin-Lof, A. (eds) Modern Problems in Insurance Mathematics. 2014. P. 223-237.

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