Ukrainian Mathematical Bulletin

Volume 3, Issue 2, 2006 pp. 203-231.

On the Total Time for a Homogeneous Process with Independent Variables to Stay in an Interval

Authors: Viktor F. Kadankov, Tat'yana V. Kadankova
Author institution: Viktor Fedorovich Kadankov, Institute of Mathematics of the National Academy of Sciences of Ukraine, ul. Tereshchenkovskaya, 3, 01601, Kiev-4, Ukraine kadankov@voliacable.com Tat'yana Viktorovna Kadankova, Mathematical Statistics Center for Statistics Limburgs Universitair Centrum, Universitaire Campus, b.D, B-3590, Diepenbeek, Belgium tetyana.kadankova@uhasselt.be

Summary: For a series of homogeneous processes with independent increments, we obtain integral transformations for distributions of the total time for the processes to stay in an interval. For a symmetric Wiener process, we obtain the distribution of the total duration of stay in an interval.

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