On unimodal Lévy processes on the nonnegative integers

Toshiro WATANABE

doi:10.2969/jmsj/04420239

Toshiro WATANABE

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JOURNAL FREE ACCESS

1992 Volume 44 Issue 2 Pages 239-250

DOI https://doi.org/10.2969/jmsj/04420239

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Published: 1992 Received: October 01, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) G. Forst, A characterization of self-decomposable probabilities on the half-line, Z. Wahrsch. verw. Gebiete, 49 (1979), 349-352.
2) B. G. Hansen, On log-concave and log-convex infinitely divisible sequences and densities, Ann. Probability, 16 (1988), 1832-1839.
3) P. Holgate, The modality of some compound Poisson distributions, Biometrika, 57 (1970), 666-667.
4) S. K. Katti, Infinite divisibility of integer valued random variables, Ann. Math. Statist., 38 (1967), 1306-1308.
5) J. Keilson and H. Gerber, Some results for discrete unimodality, J. Amer. Statist. Assoc., 66 (1971), 386-389.
6) P. Medgyessy, On a new class of unimodal infinitely divisible distribution functions and related topics, Studia Sci. Math. Hungar., 2 (1967), 441-446.
7) K. Sato, Bounds of modes and unimodal processes with independent increments, Nagoya Math. J., 104 (1986), 29-42.
8) K. Sato, Behavior of modes of a class of processes with independent increments, J. Math. Soc. Japan, 38 (1986), 679-695.
9) K. Sato and M. Yamazato, On distribution functions of class L, Z. Wahrsch. verw. Gebiete, 43 (1978), 273-308.
10) F. W. Steutel, On the zeros of infinitely divisible densities, Ann. Math. Statist., 42 (1971), 812-815.
11) F. W. Steutel and K. van Harn, Discrete analogues of self-decomposability and stability, Ann. Probability, 7 (1979), 893-899.
12) T. Watanabe, Non-symmetric unimodal Lévy processes that are not of class L, Japan. J. Math., 15 (1989), 191-203.
13) T. Watanabe, On the strong unimodality of Lévy processes, Preprint.
14) S.J. Wolfe, On the unimodality of L functions, Ann. Math. Statist., 42 (1971), 912-918.
15) S. J. Wolfe, On the unimodality of infinitely divisible distribution functions, Z. Wahrsch. verw. Gebiete, 45 (1978), 329-335.
16) M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probability, 6 (1978), 523-531.
17) M. Yamazato, On strongly unimodal infinitely divisible distributions, Ann. Probability, 10 (1982), 589-601.

Right : [1] G. Forst, A characterization of self-decomposable probabilities on the half-line, Z. Wahrsch. verw. Gebiete, 49 (1979), 349-352.
[2] B. G. Hansen, On log-concave and log-convex infinitely divisible sequences and densities, Ann. Probability, 16 (1988), 1832-1839.
[3] P. Holgate, The modality of some compound Poisson distributions, Biometrika, 57 (1970), 666-667.
[4] S. K. Katti, Infinite divisibility of integer valued random variables, Ann. Math. Statist., 38 (1967), 1306-1308.
[5] J. Keilson and H. Gerber, Some results for discrete unimodality, J. Amer. Statist. Assoc., 66 (1971), 386-389.
[6] P. Medgyessy, On a new class of unimodal infinitely divisible distribution functions and related topics, Studia Sci. Math. Hungar., 2 (1967), 441-446.
[7] K. Sato, Bounds of modes and unimodal processes with independent increments, Nagoya Math. J., 104 (1986), 29-42.
[8] K. Sato, Behavior of modes of a class of processes with independent increments, J. Math. Soc. Japan, 38 (1986), 679-695.
[9] K. Sato and M. Yamazato, On distribution functions of class L, Z. Wahrsch. verw. Gebiete, 43 (1978), 273-308.
[10] F. W. Steutel, On the zeros of infinitely divisible densities, Ann. Math. Statist., 42 (1971), 812-815.
[11] F. W. Steutel and K. van Harn, Discrete analogues of self-decomposability and stability, Ann. Probability, 7 (1979), 893-899.
[12] T. Watanabe, Non-symmetric unimodal Lévy processes that are not of class L, Japan. J. Math., 15 (1989), 191-203.
[13] T. Watanabe, On the strong unimodality of Lévy processes, Preprint.
[14] S. J. Wolfe, On the unimodality of L functions, Ann. Math. Statist., 42 (1971), 912-918.
[15] S. J. Wolfe, On the unimodality of infinitely divisible distribution functions, Z. Wahrsch. verw. Gebiete, 45 (1978), 329-335.
[16] M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probability, 6 (1978), 523-531.
[17] M. Yamazato, On strongly unimodal infinitely divisible distributions, Ann. Probability, 10 (1982), 589-601.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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