Volume 70 of the series Lecture Notes in Biomathematics pp 210221
Unimodality and Bounds of Modes for Distributions of Generalized Sojourn Times
 Keniti SatoAffiliated withDepartment of Mathematics, College of General Education, Nogoya University
Summary
The distribution of the generalized sojourn time T for a birthanddeath process up to the first passage time to the state n, starting at the state m (m < n), is considered. The generalized sojourn time is the sum of the sojourn times at the states i, over i = 0,1,...,n−1, with a statedependent signed weight. A main new result of the paper is that the distribution of T is unimodal. Explicit description of the distribution is given by using exponential distributions on the positive and the negative axis. Bounds of the mode are derived from this description. Other bounds of the modes of general unimodal distributions are given in terms of absolute moments and central absolute moments. Infinite divisibility of T is also proved. These results are extended to generalized sojourn times of diffusion processes, which arise in models of neurobiology and population genetics.
 Title
 Unimodality and Bounds of Modes for Distributions of Generalized Sojourn Times
 Book Title
 Stochastic Methods in Biology
 Book Subtitle
 Proceedings of a Workshop held in Nagoya, Japan July 8–12 1985
 Book Part
 V
 Pages
 pp 210221
 Copyright
 1987
 DOI
 10.1007/9783642465994_17
 Print ISBN
 9783540176480
 Online ISBN
 9783642465994
 Series Title
 Lecture Notes in Biomathematics
 Series Volume
 70
 Series ISSN
 0341633X
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
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 Editors

 Motoo Kimura ^{(1)}
 Gopinath Kallianpur ^{(2)}
 Takeyuki Hida ^{(3)}
 Editor Affiliations

 1. National Institute of Genetics
 2. Center for Stochastic Processes, Department of Statistics, University of North Carolina
 3. Department of Mathematics, Faculty of Science, Nagoya University
 Authors

 Keniti Sato ^{(4)}
 Author Affiliations

 4. Department of Mathematics, College of General Education, Nogoya University, Nagoya, Japan
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