Behavior of modes of a class of processes with independent increments

Ken-iti SATO

doi:10.2969/jmsj/03840679

Ken-iti SATO

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JOURNAL FREE ACCESS

1986 Volume 38 Issue 4 Pages 679-695

DOI https://doi.org/10.2969/jmsj/03840679

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Published: 1986 Received: April 16, 1985 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) W. Feller, An introduction to probability theory and its applications, Vol. II, Second edition, Wiley, New York, 1971.
2) B. E. Fristedt, Sample function behavior of increasing processes with stationary, independent increments, Pacific J. Math., 21 (1967), 21-33.
3) B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables (English translation), Second edition, Addison-Wesley, Reading, 1968.
4) P. Hall, On the limiting behaviour of the mode and median of a sum of independent random variables, Ann. Probab., 8 (1980), 419-430.
5) K. Sato, Bounds of modes and unimodal processes with independent increments, Nagoya Math. J., 104 (1986), 29-42.
6) K. Sato and M. Yamazato, On distribution functions of class L, Z. Wahrsch. Verw. Gebiete, 43 (1978), 273-308.
7) E. Seneta, Regularly varying functions, Lecture Notes in Math., 508, Springer, 1976.
8) S. J. Wolfe, Inequalities for modes of L functions, Ann. Math. Statist., 42 (1971), 2126-2130.
9) M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probab., 6(1978), 523-531.
10) V. M. Zolotarev, On the asymptotic behaviour of a class of infinitely divisible laws, Theory Probab. Appl., 6 (1961), 304-307.
11) V. M. Zolotarev, One-dimensional stable distributions (in Russian), Nauka, Moscow, 1983.

Right : [1] W. Feller, An introduction to probability theory and its applications, Vol. II, Second edition, Wiley, New York, 1971.
[2] B. E. Fristedt, Sample function behavior of increasing processes with stationary, independent increments, Pacific J. Math., 21 (1967), 21-33.
[3] B. V. Gnedenko and A. N. Kolmogorov, Limit distributions for sums of independent random variables (English translation), Second edition, Addison-Wesley, Reading, 1968.
[4] P. Hall, On the limiting behaviour of the mode and median of a sum of independent random variables, Ann. Probab., 8 (1980), 419-430.
[5] K. Sato, Bounds of modes and unimodal processes with independent increments, Nagoya Math. J., 104 (1986), 29-42.
[6] K. Sato and M. Yamazato, On distribution functions of class L, Z. Wahrsch. Verw. Gebiete, 43 (1978), 273-308.
[7] E. Seneta, Regularly varying functions, Lecture Notes in Math., 508, Springer, 1976.
[8] S. J. Wolfe, Inequalities for modes of L functions, Ann. Math. Statist., 42 (1971), 2126-2130.
[9] M. Yamazato, Unimodality of infinitely divisible distribution functions of class L, Ann. Probab., 6 (1978), 523-531.
[10] V. M. Zolotarev, On the asymptotic behaviour of a class of infinitely divisible laws, Theory Probab. Appl., 6 (1961), 304-307.
[11] V. M. Zolotarev, One-dimensional stable distributions (in Russian), Nauka, Moscow, 1983.

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

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