On some generalizations of the results about the distribution of the maximum of the Chentsov random field on polygonal lines
Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 73-83.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we compute the probability $\mathbf{P}\left\{\sup_{t\in [T_1,T_2]}(w(t)-h(t))0\right\},$ where $w(t)$ is a Wiener process and $h$ is a step-wise linear function. We use it to obtain the distribution of the maximum of the Chentsov random field on polygonal lines. We have considerably expanded a class of such polygonal lines in this paper.
Keywords: Wiener process; Chentsov random field; distribution of the supremum.
@article{THSP_2016_21_1_a7,
     author = {N. V. Prokhorenko (Kruglova)},
     title = {On some generalizations of the results about the distribution of the maximum of the {Chentsov} random field on polygonal lines},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {73--83},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a7/}
}
TY  - JOUR
AU  - N. V. Prokhorenko (Kruglova)
TI  - On some generalizations of the results about the distribution of the maximum of the Chentsov random field on polygonal lines
JO  - Teoriâ slučajnyh processov
PY  - 2016
SP  - 73
EP  - 83
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a7/
LA  - en
ID  - THSP_2016_21_1_a7
ER  - 
%0 Journal Article
%A N. V. Prokhorenko (Kruglova)
%T On some generalizations of the results about the distribution of the maximum of the Chentsov random field on polygonal lines
%J Teoriâ slučajnyh processov
%D 2016
%P 73-83
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a7/
%G en
%F THSP_2016_21_1_a7
N. V. Prokhorenko (Kruglova). On some generalizations of the results about the distribution of the maximum of the Chentsov random field on polygonal lines. Teoriâ slučajnyh processov, Tome 21 (2016) no. 1, pp. 73-83. http://geodesic.mathdoc.fr/item/THSP_2016_21_1_a7/

[1] J. L. Doob, “Heuristic approach to Kolmogorov-Smirnov theorems”, Ann. Math. Statist., 20 (1949), 393–403 | DOI | MR | Zbl

[2] S. Malmquist, “On certain confidence contours for distribution functions”, Ann. Math. Statist., 25 (1954), 523–533 | DOI | MR | Zbl

[3] S. R. Paranjape, C. Park, “Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary”, J. Appl. Probab., 10:4 (1973), 875–880 | DOI | MR | Zbl

[4] C. Park, F. J. Schuurmann, “Evaluations of barrier-crossing probabilities of Wiener paths”, J. Appl. Prob., 13 (1976), 267–275 | DOI | MR | Zbl

[5] C. Park, D. L. Skoug, “Distribution estimates of barrier-crossing probabilities of the Yeh-Wiener process”, Pacific J. Math., 78:2 (1978), 455–466 | DOI | MR | Zbl

[6] I. I. Klesov, “On the probability of attainment of a curvilinear level by a Wiener field”, Probab. and Math. Statist., 51 (1995), 63–67 | MR

[7] N. V. Kruglova, “Distribution of the maximum of the Chentsov random field”, Theor. Stoch. Proc., 14(30):1 (2008), 76–81 | MR | Zbl

[8] O. I. Klesov, N. V. Kruglova, “The distribution of a functional of the Wiener process and its application to the Brownian sheet”, Statistics, 45:1 (2011), 19–26 | DOI | MR | Zbl