Asymptotic behavior of the distribution of the maximum of a Chentsov field on polygonal lines

Author:
N. V. Kruglova

Translated by:
S. Kvasko

Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom **81** (2010).

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

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a two-parameter Chentsov field. The asymptotic behavior of the tail of the distribution of the maximum of the field on a polygonal line with several linear sections is found in the paper.

**1.**N. N. Chentsov,*Wiener random fields of several parameters*, Dokl. Akad. Nauk SSSR**46**(1956), no. 4, 607-609. (Russian)**2.**Endre Csáki, Davar Khoshnevisan, and Zhan Shi,*Boundary crossings and the distribution function of the maximum of Brownian sheet*, Stochastic Process. Appl.**90**(2000), no. 1, 1–18. MR**1787122**, https://doi.org/10.1016/S0304-4149(00)00031-4**3.**Victor Goodman,*Distribution estimates for functionals of the two-parameter Wiener process*, Ann. Probability**4**(1976), no. no 6, 977–982. MR**0423556****4.**I. I. Klesov,*On the probability of attainment of a curvilinear level by a Wiener field*, Teor. Ĭmovīr. Mat. Stat.**51**(1994), 62–66 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist.**51**(1995), 63–67 (1996). MR**1445053****5.**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)**6.**Natalia Kruglova,*Distribution of the maximum of the Chentsov random field*, Theory Stoch. Process.**14**(2008), no. 1, 76–81. MR**2479708****7.**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**0381015****8.**V. I. Piterbarg,*Gaussian random processes*, Probability theory. Mathematical statistics. Theoretical cybernetics, Vol. 19, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii, Moscow, 1982, pp. 155–199 (Russian). MR**657960****9.**J. Yeh,*Wiener measure in a space of functions of two variables*, Trans. Amer. Math. Soc.**95**(1960), 433–450. MR**0125433**, https://doi.org/10.1090/S0002-9947-1960-0125433-1

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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

DOI:
https://doi.org/10.1090/S0094-9000-2011-00813-7

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