Асимптотика распределения числа пересечений полосы для случайных процессов с независимыми приращениями

Аннотация

Subject of research: homogeneous processes with independent increments and the generalised renewal processes. Aim of the research: obtaine the complete asymptotic expansions for the distribution of the number of a rectilinear strip by trajectories of homogeneous process with independent increments and the generalised renewal process. Methods of research: in the dissertation a used the analytical factorization method. The results achivved and their novelty: all main outcomes of the thesis are new and consist of the following: - complete asymptotic expansions in t —> oo for the distribution of the number of crossings of a rectilinear strip till the moment t by a trajectory of homogeneous process with independent increments have been obtained. Thus it is supposed that strip borders grow together with t and are imposed on condition process, basically, Kramer’s type; - the first members of asymptotic decomposition are written out in an explicit form and the algorithm of calculation of the subsequent members is specified; - the results specified above are transferred in case of the generalised process of restoration. Practical value: the thesis has theoretical character. Field of application: the received results can be used at the decision of various problems of mathematical statistics, the theory of mass service, the theory of storage of stocks and others.