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Sibirsk. Mat. Zh., 2015, Volume 56, Number 1, Pages 36–64 (Mi smj2620)  

This article is cited in 16 scientific papers (total in 16 papers)

Large deviation principles for the finite-dimensional distributions of compound renewal processes

A. A. Borovkov, A. A. Mogul'skiĭ

Sobolev Institute of Mathematics, Novosibirsk, Russia

Abstract: The paper deals with the large deviation probabilities for compound renewal processes. We establish the local and “integral” principles of large deviations in the state space of the process (i.e. for the value of the process at time $T$ as $T\to\infty$). We also find conditions for asymptotically weak dependence of the increments of the processes (in the crude asymptotics sense) and prove the local and “integral” principles of large deviations for the finite-dimensional distributions of the process.

Keywords: compound renewal process, compound renewal process with stationary increments, renewal function, deviation rate function, second deviation rate function, large deviation principle, local large deviation principle.

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English version:
Siberian Mathematical Journal, 2015, 56:1, 28–53

Bibliographic databases:

UDC: 519.21
Received: 25.08.2014

Citation: A. A. Borovkov, A. A. Mogul'skiǐ, “Large deviation principles for the finite-dimensional distributions of compound renewal processes”, Sibirsk. Mat. Zh., 56:1 (2015), 36–64; Siberian Math. J., 56:1 (2015), 28–53

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Borovkov, A. A. Mogul'skii, “Large deviation principles for trajectories of compound renewal processes. I”, Theory Probab. Appl., 60:2 (2016), 207–221  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. A. Borovkov, A. A. Mogul'skii, “Large deviation principles for trajectories of compound renewal processes. II”, Theory Probab. Appl., 60:3 (2016), 349–366  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. A. Borovkov, “Large deviation principles in boundary problems for compound renewal processes”, Siberian Math. J., 57:3 (2016), 442–469  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. I”, Siberian Math. J., 59:3 (2018), 383–402  mathnet  crossref  crossref  isi  elib
    5. A. A. Borovkov, A. A. Mogulskii, “Integro-local limit theorems for compound renewal processes under Cramér's condition. II”, Siberian Math. J., 59:4 (2018), 578–597  mathnet  crossref  crossref  isi  elib
    6. A. A. Mogulskii, E. I. Prokopenko, “Integro-lokalnye teoremy dlya mnogomernykh obobschennykh protsessov vosstanovleniya pri momentnom uslovii Kramera. I”, Sib. elektron. matem. izv., 15 (2018), 475–502  mathnet  crossref
    7. A. A. Mogulskii, “Lokalnye teoremy dlya arifmeticheskikh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektron. matem. izv., 16 (2019), 21–41  mathnet  crossref
    8. A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo pervogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1464–1477  mathnet  crossref
    9. A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii v fazovom prostranstve dlya mnogomernogo vtorogo obobschennogo protsessa vosstanovleniya”, Sib. elektron. matem. izv., 16 (2019), 1478–1492  mathnet  crossref
    10. A. A. Mogul'skiǐ, E. I. Prokopenko, “Local theorems for arithmetic multidimensional compound renewal processes under Cramér's condition”, Siberian Adv. Math., 30:4 (2020), 284–302  mathnet  crossref  crossref
    11. A. A. Borovkov, “On Large Deviation Principles for Compound Renewal Processes”, Math. Notes, 106:6 (2019), 864–871  mathnet  crossref  crossref  mathscinet  isi  elib
    12. A. A. Borovkov, “Integro-local theorems in boundary crossing problems for compound renewal processes”, Siberian Math. J., 60:6 (2019), 957–972  mathnet  crossref  crossref  isi  elib
    13. A. A. Borovkov, A. A. Mogul'skii, E. I. Prokopenko, “Properties of the deviation rate function and the asymptotics for the Laplace thansform of the distribution of a compound renewal process”, Theory Probab. Appl., 64:4 (2020), 499–512  mathnet  crossref  crossref  mathscinet  isi  elib
    14. A. A. Mogulskii, E. I. Prokopenko, “Printsip bolshikh uklonenii dlya konechnomernykh raspredelenii mnogomernykh obobschennykh protsessov vosstanovleniya”, Matem. tr., 23:2 (2020), 148–176  mathnet  crossref
    15. A. A. Borovkov, “Tochnaya asimptotika preobrazovaniya Laplasa nad raspredeleniem obobschennogo protsessa vosstanovleniya i svyazannye s nei zadachi”, Sib. elektron. matem. izv., 17 (2020), 824–839  mathnet  crossref
    16. A. V. Logachev, A. A. Mogulskii, “Lokalnye teoremy dlya konechnomernykh priraschenii arifmeticheskikh mnogomernykh obobschennykh protsessov vosstanovleniya pri vypolnenii usloviya Kramera”, Sib. elektron. matem. izv., 17 (2020), 1766–1786  mathnet  crossref
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