Local Times of Bernoulli Walk |
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| Authors: | JC de Vos W Vervaat |
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| Institution: | Department of Economics Catholic University of Brabant P.O. Box 90153 5000 LE Tilburg The Netherlands;Department of Mathematics Catholic University of Nijmegen Toernooiveld 5 6525 ED Nijmegen The Netherlands |
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| Abstract: | The joint probability generating functions of local times of Bernoulli walk at various stopping times are determined by simple functional equations. The results can be interpreted by means of branching processes with immigration satisfying the same equations. One way of working with these results is to specialize and evaluate the derived equations, but a more elegant and efficient way is to compare these equations with corresponding functional equations for branching processes. |
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| Keywords: | local time ascending local time descending local time probability generating function shift equation excursion branching process immigration extinction |
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