Asymptotic behavior of the distribution of the maximum of a Chentsov field on polygonal lines
Author:
N. V. Kruglova
Translated by:
S. Kvasko
Journal:
Theor. Probability and Math. Statist. 81 (2010), 101-115
MSC (2010):
Primary 60G15, 60G60
DOI:
https://doi.org/10.1090/S0094-9000-2011-00813-7
Published electronically:
January 20, 2011
MathSciNet review:
2667313
Full-text PDF Free Access
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Abstract: Let $X(s,t)$ be a two-parameter Chentsov field. The asymptotic behavior of the tail of the distribution of the maximum of the field $X(s,t)$ on a polygonal line with several linear sections is found in the paper.
References
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- O. I. Klesov and N. V. Kruglova, The distribution of functionals such as the maximum for a two-parameter Chentsov field, Naukovi Visti NTUU (KPI) 2007, no. 4, 136–141. (Ukrainian)
- Natalia Kruglova, Distribution of the maximum of the Chentsov random field, Theory Stoch. Process. 14 (2008), no. 1, 76–81. MR 2479708
- S. R. Paranjape and C. Park, Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary, J. Appl. Probability 10 (1973), 875–880. MR 381015, DOI https://doi.org/10.2307/3212390
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References
- N. N. Chentsov, Wiener random fields of several parameters, Dokl. Akad. Nauk SSSR 46 (1956), no. 4, 607–609. (Russian)
- E. Csaki, D. Khoshnevisan, and Z. Shi, Boundary crossings and the distribution function of the maximum of Brownian sheet, Stoch. Process. Appl. 90 (2000), no. 1, 1–18. MR 1787122 (2001m:60115)
- V. Goodman, Distribution estimates for functionals of the two-parameter Wiener process, Ann. Probab. 4 (1976), no. 6, 977–982. MR 0423556 (54:11532)
- I. I. Klesov, On the probability of attainment of a curvilinear level by a Wiener field, Teor. Ĭmovir. Mat. Stat. 51 (1994), 62–66; English transl. in Theory Probab. Math. Statist. 51 (1995), 63–67. MR 1445053 (97m:60074)
- O. I. Klesov and N. V. Kruglova, The distribution of functionals such as the maximum for a two-parameter Chentsov field, Naukovi Visti NTUU (KPI) 2007, no. 4, 136–141. (Ukrainian)
- N. V. Kruglova, Distribution of the maximum of the Chentsov random field, Theor. Stoch. Process. 14 (2008), no. 1, 76–81. MR 2479708 (2009m:60119)
- S. R. Paranjape and C. Park, Distribution of the supremum of the two-parameter Yeh–Wiener process on the boundary, Appl. Probab. 10 (1973), no. 4, 875–880. MR 0381015 (52:1912)
- V. I. Piterbarg, Gaussian random processes, Probability theory. Mathematical statistics. Theoretical cybernetics, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii (1982), no. 19, 155–199. MR 657960 (84h:60077)
- J. Yeh, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. (1960), no. 95, 433–450. MR 0125433 (23:A2735)
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Additional Information
N. V. Kruglova
Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty for Physics and Mathematics, National Technical University of Ukraine (KPI), Peremogy Avenue 37, Kyiv 03056, Ukraine
Email:
natahak@ukr.net
Keywords:
Chentsov field,
distribution of the maximum,
Gaussian processes
Received by editor(s):
September 22, 2009
Published electronically:
January 20, 2011
Article copyright:
© Copyright 2011
American Mathematical Society
