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Mat. Zametki, 2015, Volume 97, Issue 6, Pages 868–883 (Mi mz10487)  

This article is cited in 7 scientific papers (total in 7 papers)

On the Asymptotic Laplace Method and Its Application to Random Chaos

D. A. Korshunovab, V. I. Piterbargc, E. Hashorvad

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Lancaster University, United Kingdom
c Lomonosov Moscow State University
d University of Lausanne, Switzerland

Abstract: The asymptotics of the multidimensional Laplace integral for the case in which the phase attains its minimum on an arbitrary smooth manifold is studied. Applications to the study of the asymptotics of the distribution of Gaussian and Weibullian random chaoses are considered.

Keywords: Laplace asymptotic method, Gaussian chaos, Weibullian chaos, Gelfand–Leray differential form, random chaos.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00050-a
14-01-00075
Swiss National Science Foundation 200021-1401633/1
200021-134785
European Union's Seventh Framework Programme RARE-318984
The work of the first and third authors was supported by the Swiss National Science Foundation (projects 200021-1401633/1 and 200021-134785). The work of the second author was supported by the Russian Foundation for Basic Research (grants no. 11-01-00050-a and no. 14-01-00075). The work of all authors was also supported by the project RARE-318984 (a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Program).


DOI: https://doi.org/10.4213/mzm10487

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English version:
Mathematical Notes, 2015, 97:6, 878–891

Bibliographic databases:

Document Type: Article
UDC: 519.21
Received: 10.04.2014

Citation: D. A. Korshunov, V. I. Piterbarg, E. Hashorva, “On the Asymptotic Laplace Method and Its Application to Random Chaos”, Mat. Zametki, 97:6 (2015), 868–883; Math. Notes, 97:6 (2015), 878–891

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. I. Rytova, E. B. Yarovaya, “Multidimensional Watson Lemma and Its Applications”, Math. Notes, 99:3 (2016), 406–412  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Piterbarg V.I., “High extrema of Gaussian chaos processes”, Extremes, 19:2 (2016), 253–272  crossref  mathscinet  zmath  isi  elib  scopus
    3. Piterbarg V.I., “Large extremes of Gaussian chaos processes”, Dokl. Math., 93:2 (2016), 145–147  crossref  mathscinet  zmath  isi  elib  scopus
    4. 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
    5. 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
    6. L. Bai, “Extremes of $L^p$-norm of vector-valued Gaussian processes with trend”, Stochastics, 90:8 (2018), 1111–1144  crossref  mathscinet  isi  scopus
    7. Bai L., “Extremes of Gaussian Chaos Processes With Trend”, J. Math. Anal. Appl., 473:2 (2019), 1358–1376  crossref  mathscinet  zmath  isi  scopus
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