Abstract
For a random function dependent on time and on a point of a space with measure, we find an asymptotic expression for the measure of the region in which values of the function do not exceed a given level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. P. Yurachkivs'kyi, “The law of large numbers for the measure of a region covered by a flow of random sets,”Teor. Ver. Mat. Statist., Issue 55, 173–177 (1996).
A. P. Yurachkivs'kyi, “Averaging phenomena for unions of random sets,”Dokl. Akad. Nauk Ukr., No. 6, 45–49 (1997).
A. P. Yurachkivs'kyi, “Limit theorems for the measures of sections of random sets,”Teor. Ver. Mat. Statist., Issue 56, 177–182 (1997).
A. P. Yurachkivs'kyi, “Functional limit theorems for coverage processes,”Theory Stoch. Process.,3(19) No. 3-4, 256–263 (1997).
A. P. Yurachkivs'kyi, “Functional limit theorems with Poisson component in the problems of stochastic geometry,”Dokl. Akad. Nauk Ukr., No. 11, 46–50 (1997).
J. Jacod and A. N. Shiryaev,Limit Theorems for Random Processes [in Russian], Fizmatgiz, Moscow (1994).
A. V. Skorokhod, “Limit theorems for random processes”Teor. Ver. Primen. 1, No. 2, 289–319 (1956).
R. Sh. Liptser and A. N. Shiryaev,Theory of Martingales [in Russian], Nauka, Moscow (1986).
A. N. Shiryaev,Probability [in Russian], Nauka, Moscow (1989).
V. V. Petrov,Sums of Independent Random Variables [in Russian], Nauka, Moscow (1972).
Additional information
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 4, pp. 542–552, April, 1999.
Rights and permissions
About this article
Cite this article
Yurachkivs'kyi, A.P. A functional limit theorem of the type of the law of large numbers for random reliefs. Ukr Math J 51, 604–617 (1999). https://doi.org/10.1007/BF02591762
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02591762