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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/6203

Title: Intersections of an interval by a process with independent increments
Authors: KADANKOVA, Tetyana
Kadankov, V.F.
Issue Date: 2005
Citation: Theory of stochastic processes, 11(27). p. 54-68
Abstract: In this article we determine the Laplace transforms of the one-boundary characteristics and of the distribution of the number of intersections of a fixed interval by a difference of a compound Poisson process and a compound renewal process. The results obtained are applied for a particular case of this process, namely, for the difference of the compound Poisson proces and the renewal process whose jumps are geometrically distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process. In this case, under certain assumptions, we find the limit distributions of the one-boundary and two-boundary characteristics of the process. In addition, we prove the weak convergence of these distributions to the corresponding distributions of a symmetric Wiener process.
URI: http://hdl.handle.net/1942/6203
Category: A2
Type: Journal Contribution
Appears in Collections: Research publications

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