Special operator equations

M. M. Lavrent'ev; L. Ya Savel'ev; S. V. Balakin

doi:10.1134/S1990478909020100

Special operator equations

M. M. Lavrent'ev, L. Ya Savel'ev, S. V. Balakin

Research output: Contribution to journal › Article › Research › peer-review

Abstract

The study addresses the matrix operator equations of a special form which are used in the theory of Markov chains. Solving the operator equations with stochastic transition probability matrices of large finite or even countably infinite size reduces to the case of stochastic matrices of small size. In particular, the case of ternary chains is considered in detail. A Markov model for crack growth in a composite serves as an example of application.

Original language	English
Pages (from-to)	246-258
Number of pages	13
Journal	Journal of Applied and Industrial Mathematics
Volume	3
Issue number	2
DOIs	https://doi.org/10.1134/S1990478909020100
Publication status	Published - 2009
Externally published	Yes

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title = "Special operator equations",

abstract = "The study addresses the matrix operator equations of a special form which are used in the theory of Markov chains. Solving the operator equations with stochastic transition probability matrices of large finite or even countably infinite size reduces to the case of stochastic matrices of small size. In particular, the case of ternary chains is considered in detail. A Markov model for crack growth in a composite serves as an example of application.",

author = "Lavrent'ev, {M. M.} and Savel'ev, {L. Ya} and Balakin, {S. V.}",

note = "Funding Information: The authors were supported by the Russian Foundation for Basic Research (project no. 06– 01–00422), the State Maintenance Program for the Leading Scientific Schools (project no. NSh– 7157.2006.1), and the Siberian Division of the Russian Academy of Sciences (Interdisciplinary project no. 2006–48).",

year = "2009",

doi = "10.1134/S1990478909020100",

language = "English",

volume = "3",

pages = "246--258",

journal = "Journal of Applied and Industrial Mathematics",

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AU - Lavrent'ev, M. M.

AU - Savel'ev, L. Ya

AU - Balakin, S. V.

N1 - Funding Information: The authors were supported by the Russian Foundation for Basic Research (project no. 06– 01–00422), the State Maintenance Program for the Leading Scientific Schools (project no. NSh– 7157.2006.1), and the Siberian Division of the Russian Academy of Sciences (Interdisciplinary project no. 2006–48).

PY - 2009

Y1 - 2009

N2 - The study addresses the matrix operator equations of a special form which are used in the theory of Markov chains. Solving the operator equations with stochastic transition probability matrices of large finite or even countably infinite size reduces to the case of stochastic matrices of small size. In particular, the case of ternary chains is considered in detail. A Markov model for crack growth in a composite serves as an example of application.

AB - The study addresses the matrix operator equations of a special form which are used in the theory of Markov chains. Solving the operator equations with stochastic transition probability matrices of large finite or even countably infinite size reduces to the case of stochastic matrices of small size. In particular, the case of ternary chains is considered in detail. A Markov model for crack growth in a composite serves as an example of application.

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DO - 10.1134/S1990478909020100

M3 - Article

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SN - 1990-4789

VL - 3

SP - 246

EP - 258

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

IS - 2

ER -

Special operator equations

Abstract

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