Limit theorems for point processes and their functionals

Yuji KASAHARA; Shinzo WATANABE

doi:10.2969/jmsj/03830543

Yuji KASAHARA, Shinzo WATANABE

著者情報

ジャーナルフリー

1986 年 38 巻 3 号 p. 543-574

DOI https://doi.org/10.2969/jmsj/03830543

詳細

Published: 1986 Received: 1985/07/15 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) P. Billingsley, Weak Convergence of Probability Measures, Wiley, New York, 1971.
2) T. Brown, A martingale approach to the Poisson convergence of simple point processes, Ann. Probability, 6 (1978), 615-628.
3) T. C. Brown, Some Poisson approximations using compensators, Ann. Probability, 11 (1983), 726-744.
4) C. Dellacherie and P. A. Meyer, Probabilités et Potentiel B, Hermann, Paris, 1980.
5) R. Durrett and S. I. Resnick, Functional limit theorems for dependent variables, Ann. Probability, 6 (1978), 829-846.
6) B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, Mass., 1968 (English transl.).
7) N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam/Kodansha, Tokyo, 1981.
8) J. Jacod, Processus à accroissements indépendants: Une condition nécessaire et suffisante de convergence en loi, Z. Wahrsch. Verw. Gebiete, 63 (1983), 109-136.
9) P. Jagers, Aspects of random measures and point processes, Adv. Probab. Related Topics, 3, Marcel Dekker, New York, 1974, pp. 179-239.
10) Y. Kabanov, R. Liptser and A. Shiryayev, Some limit theorems for simple point processes (martingale approach), Stochastics, 3 (1980), 203-216.
11) O. Kallenberg, Random Measures, Academic Press, London, 1975.
12) Y. Kasahara, A note on sums and the maxima of independent, identically distributed random variables, Proc. Japan Acad. Ser. A, 60 (1984), 353-356.
13) Y. Kasahara and M. Maejima, Functional limit theorems for weighted sums of i.i.d. random variables, preprint.
14) E. Lenglart, Relation de domination entre deux Processus, Ann. Inst. H. Poincaré Sect. B, 13 (1977), 171-179.
15) T. Lindvall, Weak convergence of probability measures and random functions in the function space D[0, ∞), J. Appl. Probability, 10 (1973), 109-121.
16) R. Liptser and A. Shiryayev, A functional limit theorem for semimartingales, Theor. Probability Appl., 15 (1980), 667-688 (English transi.).
17) R. Rebolledo, La méthode des martingales appliquée à l'étude de la convergence en loi de Processus, Bull. Soc. Math. France, Mémoire, 62 (1979).
18) A. Rényi, Remarks on the Poisson process, Studia Sci. Math. Hungar., 2 (1967), 119-123.
19) A. V. Skorohod, Limit theorems for stochastic processes with independent increments, Theor. Probability Appl., 2 (1956), 138-171 (English transl.).
20) W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res., 5 (1980), 67-85.

Right : [1] P. Billingsley, Weak Convergence of Probability Measures, Wiley, New York, 1971.
[2] T. Brown, A martingale approach to the Poisson convergence of simple point processes, Ann. Probability, 6 (1978), 615-628.
[3] T. C. Brown, Some Poisson approximations using compensators, Ann. Probability, 11 (1983), 726-744.
[4] C. Dellacherie and P. A. Meyer, Probabilités et Potentiel B, Hermann, Paris, 1980.
[5] R. Durrett and S. I. Resnick, Functional limit theorems for dependent variables, Ann. Probability, 6 (1978), 829-846.
[6] B. V. Gnedenko and A. N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Reading, Mass., 1968 (English transl.).
[7] N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam/Kodansha, Tokyo, 1981.
[8] J. Jacod, Processus à accroissements indépendants: Une condition nécessaire et suffisante de convergence en loi, Z. Wahrsch. Verw. Gebiete, 63 (1983), 109-136.
[9] P. Jagers, Aspects of random measures and point processes, Adv. Probab. Related Topics, 3, Marcel Dekker, New York, 1974, pp. 179-239.
[10] Y. Kabanov, R. Liptser and A. Shiryayev, Some limit theorems for simple point processes (martingale approach), Stochastics, 3 (1980), 203-216.
[11] O. Kallenberg, Random Measures, Academic Press, London, 1975.
[12] Y. Kasahara, A note on sums and the maxima of independent, identically distributed random variables, Proc. Japan Acad. Ser. A, 60 (1984), 353-356.
[13] Y. Kasahara and M. Maejima, Functional limit theorems for weighted sums of i. i. d. random variables, preprint.
[14] E. Lenglart, Relation de domination entre deux processus, Ann. Inst. H. Poincaré Sect. B, 13 (1977), 171-179.
[15] T. Lindvall, Weak convergence of probability measures and random functions in the function space D[0, ∞), J. Appl. Probability, 10 (1973), 109-121.
[16] R. Liptser and A. Shiryayev, A functional limit theorem for semimartingales, Theor. Probability Appl., 15 (1980), 667-688 (English transi.).
[17] R. Rebolledo, La méthode des martingales appliquée à l'étude de la convergence en loi de processus, Bull. Soc. Math. France, Mémoire, 62 (1979).
[18] A. Rényi, Remarks on the Poisson process, Studia Sci. Math. Hungar., 2 (1967), 119-123.
[19] A. V. Skorohod, Limit theorems for stochastic processes with independent increments, Theor. Probability Appl., 2 (1956), 138-171 (English transl.).
[20] W. Whitt, Some useful functions for functional limit theorems, Math. Oper. Res., 5 (1980), 67-85.

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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