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Teor. Veroyatnost. i Primenen., 2003, Volume 48, Issue 4, Pages 811–818 (Mi tvp259)  

This article is cited in 12 scientific papers (total in 12 papers)

Short Communications

Limit theorem for high level $a$-upcrossings by $\chi$-process

V. I. Piterbarga, S. Stamatovićb

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Montenegro

Abstract: This paper proves the Poisson limit theorem for a number of large excursions of the modulus of the Gaussian vector process with independent identically distributed increments.

Keywords: Gaussian process, large excursion, $\chi$-square process.

DOI: https://doi.org/10.4213/tvp259

Full text: PDF file (751 kB)
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English version:
Theory of Probability and its Applications, 2004, 48:4, 734–741

Bibliographic databases:

Received: 12.11.2002

Citation: V. I. Piterbarg, S. Stamatović, “Limit theorem for high level $a$-upcrossings by $\chi$-process”, Teor. Veroyatnost. i Primenen., 48:4 (2003), 811–818; Theory Probab. Appl., 48:4 (2004), 734–741

Citation in format AMSBIB
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\by V.~I.~Piterbarg, S.~Stamatovi\'c
\paper Limit theorem for high level $a$-upcrossings
by $\chi$-process
\jour Teor. Veroyatnost. i Primenen.
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\vol 48
\issue 4
\pages 811--818
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\zmath{https://zbmath.org/?q=an:1064.60067}
\transl
\jour Theory Probab. Appl.
\yr 2004
\vol 48
\issue 4
\pages 734--741
\crossref{https://doi.org/10.1137/S0040585X97980786}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Stamatovic B., Stamatovic S., “Cox limit theorem for large excursions of a norm of a Gaussian vector process”, Statistics & Probability Letters, 80:19–20 (2010), 1479–1485  crossref  mathscinet  zmath  isi  scopus
    2. Tan Zh., Hashorva E., “Exact Asymptotics and Limit Theorems for Supremum of Stationary Chi-Processes Over a Random Interval”, Stoch. Process. Their Appl., 123:8 (2013), 2983–2998  crossref  mathscinet  zmath  isi  elib  scopus
    3. Tan Zh., Hashorva E., “Limit Theorems for Extremes of Strongly Dependent Cyclo-Stationary Chi-Processes”, Extremes, 16:2 (2013), 241–254  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tan Zh. Wu Ch., “Limit Laws For the Maxima of Stationary Chi-Processes Under Random Index”, Test, 23:4 (2014), 769–786  crossref  mathscinet  zmath  isi  scopus
    5. Piterbarg V.I., Zhdanov A., “On Probability of High Extremes For Product of Two Independent Gaussian Stationary Processes”, Extremes, 18:1 (2015), 99–108  crossref  mathscinet  zmath  isi  scopus
    6. A. I. Zhdanov, “On probability of high extremes for product of two Gaussian stationary processes”, Theory Probab. Appl., 60:3 (2016), 520–527  mathnet  crossref  crossref  mathscinet  isi  elib
    7. Piterbarg V.I., “High extrema of Gaussian chaos processes”, Extremes, 19:2 (2016), 253–272  crossref  mathscinet  zmath  isi  elib  scopus
    8. Piterbarg V.I., “Large extremes of Gaussian chaos processes”, Dokl. Math., 93:2 (2016), 145–147  crossref  mathscinet  zmath  isi  elib  scopus
    9. Ling Ch., Tan Zh., “On maxima of chi-processes over threshold dependent grids”, Statistics, 50:3 (2016), 579–595  crossref  mathscinet  zmath  isi  elib  scopus
    10. A. I. Zhdanov, V. I. Piterbarg, “High extremes of Gaussian chaos processes: a discrete time approximation approach”, Theory Probab. Appl., 63:1 (2018), 1–21  mathnet  crossref  crossref  isi  elib
    11. A. O. Kleban, V. I. Piterbarg, “Method of moments for exit probabilities of Gaussian vector processes from a large region”, Theory Probab. Appl., 63:4 (2019), 545–555  mathnet  crossref  crossref  isi  elib
    12. Zakharov V A. Chernoyarov V O. Salnikova V A. Faulgaber A.N., “The Distribution of the Absolute Maximum of the Discontinuous Stationary Random Process With Raileigh and Gaussian Components”, Eng. Lett., 27:1 (2019), 53–65  mathscinet  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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