### Abstract

Problems of convergence and stability of Bayesian estimates in the identification of stochastic control systems are considered. The informational measure of the mismatch between the estimated distribution and the estimate is the main apparatus for establishing the fact of convergence. The choice of a priori distribution of parameters is not always obvious. The Kullback-Leibler information number is taken as such measure. The convergence of the estimates of the transition function of the process to the non-stationary transition function is established in this paper. The problem of synthesis of optimal strategies for dynamic systems in which there is no part of the main information needed for constructing the optimal control is also considered. It is assumed that the system contains at least one unknown parameter belonging to some parameter space. Therefore, the class of control systems considered in the article is the class of parametric adaptive systems.

Original language | English |
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Title of host publication | Computational Science and Its Applications- ICCSA 2019 - 19th International Conference, Proceedings |

Editors | Beniamino Murgante, Osvaldo Gervasi, Elena Stankova, Vladimir Korkhov, Sanjay Misra, Carmelo Torre, Eufemia Tarantino, David Taniar, Ana Maria A.C. Rocha, Bernady O. Apduhan |

Publisher | Springer |

Pages | 691-701 |

Number of pages | 11 |

ISBN (Print) | 9783030243043 |

DOIs | |

Publication status | Published - 1 Jan 2019 |

Event | 19th International Conference on Computational Science and Its Applications, ICCSA 2019 - Saint Petersburg Duration: 1 Jul 2019 → 4 Jul 2019 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11622 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Conference on Computational Science and Its Applications, ICCSA 2019 |
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Country | Russian Federation |

City | Saint Petersburg |

Period | 1/07/19 → 4/07/19 |

### Fingerprint

### Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Computational Science and Its Applications- ICCSA 2019 - 19th International Conference, Proceedings*(pp. 691-701). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 11622 LNCS). Springer. https://doi.org/10.1007/978-3-030-24305-0_51

}

*Computational Science and Its Applications- ICCSA 2019 - 19th International Conference, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 11622 LNCS, Springer, pp. 691-701, Saint Petersburg, 1/07/19. https://doi.org/10.1007/978-3-030-24305-0_51

**Parameter Estimation Problems in Markov Random Processes.** / Karelin, Vladimir; Fominyh, Alexander; Myshkov, Stanislav; Polyakova, Lyudmila.

Research output

TY - GEN

T1 - Parameter Estimation Problems in Markov Random Processes

AU - Karelin, Vladimir

AU - Fominyh, Alexander

AU - Myshkov, Stanislav

AU - Polyakova, Lyudmila

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Problems of convergence and stability of Bayesian estimates in the identification of stochastic control systems are considered. The informational measure of the mismatch between the estimated distribution and the estimate is the main apparatus for establishing the fact of convergence. The choice of a priori distribution of parameters is not always obvious. The Kullback-Leibler information number is taken as such measure. The convergence of the estimates of the transition function of the process to the non-stationary transition function is established in this paper. The problem of synthesis of optimal strategies for dynamic systems in which there is no part of the main information needed for constructing the optimal control is also considered. It is assumed that the system contains at least one unknown parameter belonging to some parameter space. Therefore, the class of control systems considered in the article is the class of parametric adaptive systems.

AB - Problems of convergence and stability of Bayesian estimates in the identification of stochastic control systems are considered. The informational measure of the mismatch between the estimated distribution and the estimate is the main apparatus for establishing the fact of convergence. The choice of a priori distribution of parameters is not always obvious. The Kullback-Leibler information number is taken as such measure. The convergence of the estimates of the transition function of the process to the non-stationary transition function is established in this paper. The problem of synthesis of optimal strategies for dynamic systems in which there is no part of the main information needed for constructing the optimal control is also considered. It is assumed that the system contains at least one unknown parameter belonging to some parameter space. Therefore, the class of control systems considered in the article is the class of parametric adaptive systems.

KW - Bayesian probability theory

KW - Kullback-Leibler information number

KW - Parameter estimation

UR - http://www.scopus.com/inward/record.url?scp=85068591717&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/parameter-estimation-problems-markov-random-processes

U2 - 10.1007/978-3-030-24305-0_51

DO - 10.1007/978-3-030-24305-0_51

M3 - Conference contribution

AN - SCOPUS:85068591717

SN - 9783030243043

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 691

EP - 701

BT - Computational Science and Its Applications- ICCSA 2019 - 19th International Conference, Proceedings

A2 - Murgante, Beniamino

A2 - Gervasi, Osvaldo

A2 - Stankova, Elena

A2 - Korkhov, Vladimir

A2 - Misra, Sanjay

A2 - Torre, Carmelo

A2 - Tarantino, Eufemia

A2 - Taniar, David

A2 - Rocha, Ana Maria A.C.

A2 - Apduhan, Bernady O.

PB - Springer

ER -