Recurrence conditions for multidimensional processes of Ornstein-Uhlenbeck type

Ken-iti SATO; Toshiro WATANABE; Makoto YAMAZATO

doi:10.2969/jmsj/04620245

Ken-iti SATO, Toshiro WATANABE, Makoto YAMAZATO

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ジャーナルフリー

1994 年 46 巻 2 号 p. 245-265

DOI https://doi.org/10.2969/jmsj/04620245

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Published: 1994 Received: 1992/11/30 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) R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Academic Press, New York, 1968.
2) H. Dym, Stationary measures for the flow of a linear differential equation driven by white noise, Trans. Amer. Math. Soc., 123 (1966), 130-164.
3) R. V. Erickson, Constant coefficient linear differential equations driven by white noise, Ann. Math. Statist., 42 (1971), 820-823.
4) J. B. Gravereaux, Probabilités de Lévy sur R^d et équations différentielles stochastiques linéaires, Université de Rennes 1, Publications des Séminaires de Mathé-matiques, Séminaire de Probabilités 1982, 42 pages.
5) Z. J. Jurek, An integral representation of operator-selfdecomposable random variables, Bull. Acad. Polon. Sér. Sci. Math., 30 (1982), 385-393.
6) Z. J. Jurek and W. Vervaat, An integral representation for selfdecomposable Banach space valued random variables, Z. Wahrsch. Verw. Gebiete, 62 (1983), 247-262.
7) U. Küchler and B. Mensch, Langevins stochastic differential equation extended by a time-delayed term, Stochastics Stochastics Rep., 40 (1992), 23-42.
8) J.-J. Liou, Recurrence and transience of Gaussian diffusion processes, Kodai Math. J., 13 (1990), 210-230.
9) K. Sato and M. Yamazato, Stationary processes of Ornstein-Uhlenbeck type, Lecture Notes in Math., 1021, Springer, 1983, pp. 541-551.
10) K. Sato and M. Yamazato, Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type, Stochastic Process. Appl., 17 (1984), 73-100.
11) K. Sato and M. Yamazato, Remarks on recurrence criteria for processes of Ornstein-Uhlenbeck type, Lecture Notes in Math., 1540, Springer, 1993, pp. 329-340.
12) T. Shiga, A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type, Probab. Theory Related Fields, 85 (1990), 425-447.
14) S. J. Wolfe, A characterization of certain stochastic integrals, Tenth Conference on Stochastic Processes and Their Applications, Contributed Papers, Stochastic Process. Appl., 12 (1982), 136.

Right : [1] R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Academic Press, New York, 1968.
[2] H. Dym, Stationary measures for the flow of a linear differential equation driven by white noise, Trans. Amer. Math. Soc., 123 (1966), 130-164.
[3] R. V. Erickson, Constant coefficient linear differential equations driven by white noise, Ann. Math. Statist., 42 (1971), 820-823.
[4] J. B. Gravereaux, Probabilités de Lévy sur R^d et équations différentielles stochastiques linéaires, Université de Rennes 1, Publications des Séminaires de Mathé-matiques, Séminaire de Probabilités 1982, 42 pages.
[5] Z. J. Jurek, An integral representation of operator-selfdecomposable random variables, Bull. Acad. Polon. Sér. Sci. Math., 30 (1982), 385-393.
[6] Z. J. Jurek and W. Vervaat, An integral representation for selfdecomposable Banach space valued random variables, Z. Wahrsch. Verw. Gebiete, 62 (1983), 247-262.
[7] U. Küchler and B. Mensch, Langevins stochastic differential equation extended by a time-delayed term, Stochastics Stochastics Rep., 40 (1992), 23-42.
[8] J. -J. Liou, Recurrence and transience of Gaussian diffusion processes, Kodai Math. J., 13 (1990), 210-230.
[9] K. Sato and M. Yamazato, Stationary processes of Ornstein-Uhlenbeck type, Lecture Notes in Math., 1021, Springer, 1983, pp. 541-551.
[10] K. Sato and M. Yamazato, Operator-selfdecomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type, Stochastic Process. Appl., 17 (1984), 73-100.
[11] K. Sato and M. Yamazato, Remarks on recurrence criteria for processes of Ornstein-Uhlenbeck type, Lecture Notes in Math., 1540, Springer, 1993, pp. 329-340.
[12] T. Shiga, A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type, Probab. Theory Related Fields, 85 (1990), 425-447.
[13] S. J. Wolfe, On a continuous analogue of the stochastic difference equation X_n=ρX_n-1+B_n, Stochastic Process. Appl., 12 (1982), 301-312.
[14] S. J. Wolfe, A characterization of certain stochastic integrals, Tenth Conference on Stochastic Processes and Their Applications, Contributed Papers, Stochastic Process. Appl., 12 (1982), 136.

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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