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Automatic Documentation and Mathematical Linguistics

Erschienen in:

01.02.2023 | INFORMATION ANALYSIS

Markov Chains, Law of Total Probability, and Recurrence Relations

verfasst von: D. V. Vinogradov

Erschienen in: Automatic Documentation and Mathematical Linguistics | Ausgabe 1/2023

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Abstract

The article describes a general method of estimating average hitting times and the associated probabilities for homogeneous finite Markov chains. Recurrence relations for the estimated values and probabilities are obtained using fundamental formulas of the law of total probability. The described method is applied to three problems of a coupled Markov chain of the VKF method; in each case, the resulting recurrence relations are solvable for exact solutions.

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Vinogradov, D.V., Mean stopping time of a pairing Markov chain with the VKF method on a linear order, Autom. Doc. Math. Linguist., 2022, vol. 56, no. 6, pp. 329–331. https://doi.org/10.3103/S0005105522060103CrossRef

Kemeny, J.G. and Snell, J.L., Finite Markov Chains, Springer, 1983.MATH

Feller, W., An Introduction to Probability Theory and Its Applications, Wiley Series in Probability and Mathematical Statistics, New York: Wiley, 3rd ed.

Vinogradov, D.V., Random generation of hypotheses in the JSM method using simple Markov chains, Autom. Doc. Math. Linguist., 2012, vol. 46, no. 5, pp. 221–228. https://doi.org/10.3103/S0005105512050044CrossRef

Vinogradov, D.V., VKF-method of hypotheses generation, Analysis of Images, Social Networks and Texts. AIST 2014, Ignatov, D., Khachay, M., Panchenko, A., Konstantinova, N., and Yavorsky, R., Eds., Communications in Computer and Information Science, vol. 436, Cham: Springer, 2014, pp. 237–248. https://doi.org/10.1007/978-3-319-12580-0_25

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Vinogradov, D.V., Strong concentration of execution time of similarity search algorithm, Materialy 8-i vserossiiskoi mul’tikonferentsii po problemam upravleniya (MKPU-2015) (Proc. 8th All-Russ. Multiconf. on Control Problems), Rostov-on-Don: Yuzhnyi Fed. Univ., 2015, vol. 1, pp. 42–45.

Titel: Markov Chains, Law of Total Probability, and Recurrence Relations
verfasst von: D. V. Vinogradov
Publikationsdatum: 01.02.2023
Verlag: Pleiades Publishing
Erschienen in: Automatic Documentation and Mathematical Linguistics / Ausgabe 1/2023
Print ISSN: 0005-1055
Elektronische ISSN: 1934-8371
DOI: https://doi.org/10.3103/S0005105523010090

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