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On the distribution of duration of stay in an interval of the semi-continuous process with independent increments. (English) Zbl 1119.60034
Summary: For a semicontinuous homogeneous process \(\xi(t)\) with independent increments the distribution of its total duration of stay in an interval is obtained. In the case where \(E\xi(1) = 0\) and \(E\xi(1)^2 <\infty\) the limit theorem on weak convergence of the time of duration of stay in an interval of the process to the distribution of the time of duration of stay of the Wiener process in the interval \((0,1)\) is obtained. For the Wiener process the distribution of the total duration of stay in an interval is found.

60G51 Processes with independent increments; Lévy processes
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