Abstract
We deal with independent random variables which are the values of a stochastic process taken at random points in time. So we have random variables depending upon a random parameter. We obtain the conditions providing the weak convergence of random lines defined by sums or maxima or bilinear forms of these random variables for almost all values of the parameter, to one and the same stochastic process. These limit stochastic processes are described.
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A. N. Chuprunov, “On the convergence in distribution of sums and maxima of independent random variables with a random parameter,”Liet. Matem. Rink.,35, No. 1, 52–64 (1995).
A. N. Chuprunov, “On the convergence in distribution of empirical processes defined by independent random processes,”Liet. Matem. Rink.,35, No. 2, 171–180 (1995).
I. I. Gikhman and A. V. Skorokhod,Introduction to the Theory of Stochastic Process, 2nd ed. [in Russian], Nauka, Moscow (1977).
B. V. Gnedenko and A. N. Kolmogorov,Limit Theorem for Sums of Independent Random Variables, Addison-Wesley, Reading, MA (1954).
V. M. Zolotarev,Modern Theory of Summation of Independent Random Variables [in Russian], Nauka, Moscow (1986).
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Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part II.
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Chuprunov, A.N. The convergence of the random lines defined by observations of a stochastic process. J Math Sci 83, 381–392 (1997). https://doi.org/10.1007/BF02400922
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DOI: https://doi.org/10.1007/BF02400922