These results explain the nature of the SQI-, PRV-, and POV-properties of the normalizing sequences under rather simple conditions, for which these properties are satisfied. Generalized renewal processes constructed from stochastic processes are studied in Sect.
In addition, we make clear, why the requirement of continuity of the paths of the underlying process is important. The results of Sects.
These sections contain a discussion of several particular questions. This chapter aims at finding nonrandom approximations a precise definition is given below of solutions of a general class of stochastic differential equations.
We follow the setting by Gihman and Skorohod [ ], however the results below are more general. In this chapter, we study the asymptotic behavior of the renewal function and that of the renewal process constructed from a random walk over a restricted domain of multidimensional time. In doing so, we essentially apply the property studied in Sect.
Verlag Springer International Publishing. Print ISBN Electronic ISBN Autoren: Prof. Buldygin Prof.
Karl-Heinz Indlekofer Prof. Oleg I. Klesov Prof.
The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background.
In real analysis, a branch of mathematics, a slowly varying function is a function of a real variable whose behaviour at infinity is in some sense similar to the behaviour of a function converging at infinity. Similarly, a regularly varying function is a function of a real variable whose. Regularly varying functions. Anders Hedegaard Jessen and Thomas Mikosch. In memoriam Tatjana Ostrogorski. Abstract. We consider some.
Readers should have completed introductory courses in analysis and probability theory. Back to search. Record created , last modified Levin, B.
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