A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Mat. Tr., 19:2 (2016), 119–157; Siberian Adv. Math., 27:3 (2017), 160

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Matematicheskie Trudy, 2016, Volume 19, Number 2, Pages 119–157
DOI: https://doi.org/10.17377/mattrudy.2016.19.205 (Mi mt308)

This article is cited in 9 scientific papers (total in 9 papers)

The large deviation principle for a compound Poisson process

A. A. Mogul'skiĭ^ab

^a Sobolev Institute of Mathematics, Novosibirsk, Russia
^b Novosibirsk State University, Novosibirsk, Russia

Full-text PDF (357 kB) Citations (9)

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DOI: https://doi.org/10.17377/mattrudy.2016.19.205

Abstract: For a compound Poisson process, under the moment Cramér condition, the extended large deviation principle is established in the space of functions of bounded variation with the Borovkov metric.

Key words: compound Poisson process, compound renewal process, Cramér condition, deviation rate function, large deviation principle, extended large deviation principle, function of bounded variation, Borovkov metric, Chebyshev-type inequality.

Funding agency	Grant number
Russian Foundation for Basic Research	14-01-00220_а

Received: 12.05.2015

English version:
Siberian Advances in Mathematics, 2017, Volume 27, Issue 3, Pages 160–186
DOI: https://doi.org/10.3103/S1055134417030026

Bibliographic databases:

Document Type: Article

UDC: 519.21

Language: Russian

Citation: A. A. Mogul'skiǐ, “The large deviation principle for a compound Poisson process”, Mat. Tr., 19:2 (2016), 119–157; Siberian Adv. Math., 27:3 (2017), 160–186

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mt308

https://www.mathnet.ru/eng/mt/v19/i2/p119

This publication is cited in the following 9 articles:

Jose Javier Cerda-Hernández, Artem Logachov, Anatoly Yambartsev, “Bid-ask spread dynamics: large upward jump with geometric catastrophes”, RAIRO-Oper. Res., 58:2 (2024), 1375
Alice Callegaro, Matthew I. Roberts, “A spatially-dependent fragmentation process”, Probab. Theory Relat. Fields, 2024
Artem Logachov, Yuri Suhov, Nikita Vvedenskaya, Anatoly Yambartsev, “A large-deviation principle for birth–death processes with a linear rate of downward jumps”, J. Appl. Probab., 2023, 1
A. A. Mogul'skiǐ, “The Extended Large Deviation Principle for the Trajectories of a Compound Renewal Process”, Sib. Adv. Math., 32:1 (2022), 35
A. A. Mogulskii, “Rasshirennyi printsip bolshikh uklonenii dlya traektorii obobschennogo protsessa vosstanovleniya”, Matem. tr., 24:1 (2021), 142–174
F. C. Klebaner, A. V. Logachov, A. A. Mogulskii, “Extended large deviation principle for trajectories of processes with independent and stationary increments on the half-line”, Problems Inform. Transmission, 56:1 (2020), 56–72
F. C. Klebaner, A. A. Mogulskii, “Large deviations for processes on half-line: Random Walk and Compound Poisson Process”, Sib. elektron. matem. izv., 16 (2019), 1–20
A. Grigor'yan, Yu. Kondratiev, A. Piatnitski, E. Zhizhina, “Pointwise estimates for heat kernels of convolution-type operators”, Proc. London Math. Soc., 117:4 (2018), 849–880
A. A. Mogul'skiǐ, “The extended large deviation principle for a process with independent increments”, Siberian Math. J., 58:3 (2017), 515–524

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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