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Avtomatika i Telemekhanika, 2004, Issue 1, Pages 50–65 (Mi at1502)  
This article is cited in 13 scientific papers (total in 13 papers)

Stochastic Systems

Analysis and estimation of the states of special Markov jump processes. I. A martingale representation

A. V. Borisovab

a Institute for Problems of Informatics RAS
b Moscow Aviation Institute (State University of Aerospace Technologies)
Full-text PDF (248 kB) Citations (13)
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Abstract: The first part of this paper was devoted to a class of continuous-time jump processes generalizing the finite-state Markov processes. Main characteristics of this process such as the transition probabilities, infinitesimal generator, and so on were established. Processes of this class were proved to be solutions of linear differential equations with a martingale in the right-hand side. Stochastic analysis of a hidden Markov model of evolution of risky assets was presented as an example.
Presented by the member of Editorial Board: B. M. Miller

Received: 01.07.2003
English version:
Automation and Remote Control, 2004, Volume 65, Issue 1, Pages 44–57
DOI: https://doi.org/10.1023/B:AURC.0000011689.11915.24
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. V. Borisov, “Analysis and estimation of the states of special Markov jump processes. I. A martingale representation”, Avtomat. i Telemekh., 2004, no. 1, 50–65; Autom. Remote Control, 65:1 (2004), 44–57
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/at1502
  • https://www.mathnet.ru/eng/at/y2004/i1/p50
    Cycle of papers
    This publication is cited in the following 13 articles:
    1. Andrey Borisov, “Filtering of hidden Markov renewal processes by continuous and counting observations”, MATH, 9:11 (2024), 30073  crossref
    2. A. V. Borisov, Yu. N. Kurinov, R. L. Smelyanskii, “Veroyatnostnyi analiz klassa markovskikh skachkoobraznykh protsessov”, Inform. i ee primen., 18:3 (2024), 30–37  mathnet  crossref
    3. A. V. Borisov, “Specific optimal estimation of special Markov jump processes”, Autom. Remote Control, 68:3 (2007), 413–429  mathnet  crossref  mathscinet  zmath
    4. Borisov A.V., “Optimal and conditionally-optimal filtering of special Markov jump processes”, SIBCON-2007: IEEE International Siberian Conference on Control and Communication, 2007, 113–119  crossref  isi
    5. A. V. Borisov, “Backward representation of Markov jump processes and related problems. I. Optimal linear estimation”, Autom. Remote Control, 67:8 (2006), 1228–1250  mathnet  crossref  mathscinet  zmath
    6. A. V. Borisov, “Analysis of hidden Markov models states generated by special jump processes”, Theory Probab. Appl., 51:3 (2007), 518–528  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. A. V. Borisov, G. B. Miller, “Analysis and filtration of special discrete-time Markov processes. I. Martingale representation”, Autom. Remote Control, 66:6 (2005), 953–962  mathnet  crossref  mathscinet  zmath
    8. Borisov A.V., Stefanovich A.I., “Optimal filtering for HMM governed by special jump processes”, 2005 44th IEEE Conference on Decision and Control & European Control Conference, IEEE Conference on Decision and Control - Proceedings, 2005, 5935–5940  crossref  isi  scopus
    9. A. V. Borisov, “Analysis and estimation of the states of special jump Markov processes. II. Optimal filtration in wiener noise”, Autom. Remote Control, 65:5 (2004), 741–754  mathnet  crossref  mathscinet  zmath  isi
    10. Borisov A., Miller G., “Hidden Markov model approach to TCP link state tracking”, 2004 43rd IEEE Conference on Decision and Control (CDC), IEEE Conference on Decision and Control - Proceedings, 2004, 3726–3731  isi
    11. Borisov A.V., “Fokker-Plank like equation for hidden Markov models governed by special jump processes”, 2004 43rd IEEE Conference on Decision and Control (CDC), IEEE Conference on Decision and Control - Proceedings, 2004, 4151–4156  isi
    12. A.V. Borisov, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004, 4151  crossref
    13. A. Borisov, G. Miller, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), 2004, 3726  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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