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On subclasses of infinitely divisible distributions on R related to hitting time distributions of 1-dimensional generalized diffusion processes

Published online by Cambridge University Press:  22 January 2016

Makoto Yamazato
Makoto Yamazato*
Affiliation:
Departmert of Mathemtics, Nagoya Institute of Technology, Showa-ku, Nagoya 466, Japan
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A distribution μ on R+ = [0, ∞) is said to be a distribution if there are an increasing (in the strict sense) sequence of positive real numbers such that, for each j = 0, …, m, there is at least one ak satisfying bj < ak < b+1 and the

Laplace transform of μ is represented as

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 127 , September 1992 , pp. 175 - 200
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

References

[ 1 ] Bondesson, L., Classes of infinitely divisible distributions and densities, Z. Wahrsch. Verw. Gebiete, 57 (1981), 39–71.CrossRefGoogle Scholar
[ 2 ] Karlin, S., Total Positivity, Vol. 1, Stanford Univ. Stanford, 1968.Google Scholar
[ 3 ] Nevanlinna, R., Paatero, V., Introduction to complex analysis, Addison-Wesley, Reading-Menlo Park-London-Don Mills, 1969.Google Scholar
[ 4 ] Sato, K., On zeros of a system of polynomials and application to sojourn time distributions of birth-and-death processes, Trans. Amer. math. Soc, 309 (1988), 375–390.CrossRefGoogle Scholar
[ 5 ] Steutel, F. W., Preservation of Infinite Divisibility under Mixing and Related Topics, Math. Centre Tracts, 33, Amsterdam, 1970.Google Scholar
[ 6 ] Thorin, O., An extension of the notion of a generalized Γ-convolution, Scand. Actuarial]., (1978), 141–149.CrossRefGoogle Scholar
[ 7 ] Yamazato, M., Strongly unimodal infinitely divisible distributions, Ann. Probab., 10 (1982), 589–601.CrossRefGoogle Scholar
[8 ] Yamazato, M., Characterization of the class of upward passage time distributions of birth and death processes and related results, J. Math. Soc. Japan, 40 (1988), 477–499.CrossRefGoogle Scholar
[9] Yamazato, M., Hitting time distributions of single points for 1-dimensional generalized diffusion processes, Nagoya Math. J., 119 (1990).CrossRefGoogle Scholar
[10] Yamazato, M., Strong unimodality of infinitely divisible distributions of class CME , submitted.Google Scholar