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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ジャーナルフリー

1986 年 38 巻 4 号 p. 679-695

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

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Published: 1986 Received: 1985/04/16 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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