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), 101115
MSC (2010):
Primary 60G15, 60G60
Published electronically:
January 20, 2011
MathSciNet review:
2667313
Fulltext PDF
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be a twoparameter 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, 607609. (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
(2001m:60115), http://dx.doi.org/10.1016/S03044149(00)000314
 3.
Victor
Goodman, Distribution estimates for functionals of the
twoparameter Wiener process, Ann. Probability 4
(1976), no. no 6, 977–982. MR 0423556
(54 #11532)
 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
(97m:60074)
 5.
O. I. Klesov and N. V. Kruglova, The distribution of functionals such as the maximum for a twoparameter Chentsov field, Naukovi Visti NTUU (KPI) 2007, no. 4, 136141. (Ukrainian)
 6.
Natalia
Kruglova, Distribution of the maximum of the Chentsov random
field, Theory Stoch. Process. 14 (2008), no. 1,
76–81. MR
2479708 (2009m:60119)
 7.
S.
R. Paranjape and C.
Park, Distribution of the supremum of the twoparameter YehWiener
process on the boundary, J. Appl. Probability 10
(1973), 875–880. MR 0381015
(52 #1912)
 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
(84h:60077)
 9.
J.
Yeh, Wiener measure in a space of functions
of two variables, Trans. Amer. Math. Soc.
95 (1960),
433–450. MR 0125433
(23 #A2735), http://dx.doi.org/10.1090/S00029947196001254331
 1.
 N. N. Chentsov, Wiener random fields of several parameters, Dokl. Akad. Nauk SSSR 46 (1956), no. 4, 607609. (Russian)
 2.
 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, 118. MR 1787122 (2001m:60115)
 3.
 V. Goodman, Distribution estimates for functionals of the twoparameter Wiener process, Ann. Probab. 4 (1976), no. 6, 977982. MR 0423556 (54:11532)
 4.
 I. I. Klesov, On the probability of attainment of a curvilinear level by a Wiener field, Teor. Ĭmovir. Mat. Stat. 51 (1994), 6266; English transl. in Theory Probab. Math. Statist. 51 (1995), 6367. MR 1445053 (97m:60074)
 5.
 O. I. Klesov and N. V. Kruglova, The distribution of functionals such as the maximum for a twoparameter Chentsov field, Naukovi Visti NTUU (KPI) 2007, no. 4, 136141. (Ukrainian)
 6.
 N. V. Kruglova, Distribution of the maximum of the Chentsov random field, Theor. Stoch. Process. 14 (2008), no. 1, 7681. MR 2479708 (2009m:60119)
 7.
 S. R. Paranjape and C. Park, Distribution of the supremum of the twoparameter YehWiener process on the boundary, Appl. Probab. 10 (1973), no. 4, 875880. MR 0381015 (52:1912)
 8.
 V. I. Piterbarg, Gaussian random processes, Probability theory. Mathematical statistics. Theoretical cybernetics, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Informatsii (1982), no. 19, 155199. MR 657960 (84h:60077)
 9.
 J. Yeh, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. (1960), no. 95, 433450. MR 0125433 (23:A2735)
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60G15,
60G60
Retrieve articles in all journals
with MSC (2010):
60G15,
60G60
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:
http://dx.doi.org/10.1090/S009490002011008137
PII:
S 00949000(2011)008137
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
