Limit theorems for generalized exceeding times, renewal and risk type processes (Q2732675)

The present paper is based on results of the author's book [``Limit theorems for composite random functions'' (Kiev, 1974)] on the theory of limit theorems for randomly stopped random processes. The generalized exceeding times were introduced in this book and the related results obtained by the author during that period were included to the book. The book was not translated into English which made access to these results difficult for many researchers. NEWLINENEWLINENEWLINEIn this paper the author introduces a general class of exceeding type functionals, called generalized exceeding times, defined on trajectories of càdlàg processes. This is a class of exceeding times determined by a family of functionals which are invariant with respect to the homogeneous transformations of time. This class of functionals includes a large number of classical models of exceeding type functionals, ruin times for risk processes in a renewal process setting among them. Functional limit theorems are studied for the exceeding type processes connected with generalized exceeding times. The results are illustrated by applications to renewal type processes, risk processes and general processes with independent increments. We refer to the extended report version of the present paper by \textit{D. S. Silvestrov} [``Generalized exceeding times, renewal and risk type processes'' (Lecture Notes No. 2, Department of Mathematical Statistics, Umeå University, 1998)].