Pseudo-differential operators and Markov processes

Takashi KOMATSU

doi:10.2969/jmsj/03630387

Takashi KOMATSU

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ジャーナルフリー

1984 年 36 巻 3 号 p. 387-418

DOI https://doi.org/10.2969/jmsj/03630387

詳細

Published: 1984 Received: 1983/03/04 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) L. Bers, F. Jones and M. Schechter, Partial Differential Equations, Lectures Appl. Math. III, Wiley, 1964.
2) A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math., 88 (1952) , 85-139.
3) A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math., 78 (1956), 289-309.
4) N. Dunford and J. Schwartz, Linear Operators, Pure Appl. Math. vol. VII, Wiley, 1963.
5) I. I. Gihman and A. V. Skorohod, The Theory of Stochastic Processes II, Grund, math. Wissen., 218, Springer-Verlag, 1975.
6) B. Grigelionis, On the Markov property of stochastic processes, (in Russian), Lietuvos Mathematikos Rinkinys, 8 (1968), 489-503.
7) B. Grigelionis, On non-linear filtering theory and absolute continuity of measures corresponding to stochastic processes, Proc. Second Japan-USSR Symp. on Probability Theory, Lecture Notes in Math., 330 (1973), Springer-Verlag, 80-94.
8) L. Hörmander, Estimates for translation invariant operators in L^p spaces, Acta Math., 104 (1960), 93-140.
9) T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math., 10 (1973), 271-303.
10) T. Komatsu, On the martingale problem for generators of stable processes with perturbations, Osaka J. Math., 21(1984), 113-132.
11) H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J., 30 (1967), 209-245.
12) P. Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, (2^e édition), 1954.
13) P. A. Meyer, Intégrales stochastiques I, II, Seminaire de Probabilités 1, Université de Strasbourg, Lecture Notes in Math., 39(1967), Springer-Verlag, 72-117.
14) D. W. Stroock, Diffusion processes associated with Lévy generators, Z. Wahr. Gebiete, 32 (1975), 209-244.
15) D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients I, II, Comm. Pure Appl. Math., 22 (1969), 345-400, 479-530.
16) D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Grund. math. Wissen., 233, Springer-Verlag, 1979.
17) M. Tsuchiya, On a small drift of Cauchy process, J. Math. Kyoto Univ., 10 (1970), 475-492.
18) M. Tsuchiya, On some perturbations of stable processes, Proc. Second Japan-USSR Symp. on Probability Theory, Lecture Notes in Math., 330 (1973), Springer-Verlag, 490-497.

Right : [1] L. Bers, F. Jones and M. Schechter, Partial Differential Equations, Lectures Appl. Math. III, Wiley, 1964.
[2] A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math., 88 (1952) , 85-139.
[3] A. P. Calderón and A. Zygmund, On singular integrals, Amer. J. Math., 78 (1956), 289-309.
[4] N. Dunford and J. Schwartz, Linear Operators, Pure Appl. Math. vol. VII, Wiley, 1963.
[5] I. I. Gihman and A. V. Skorohod, The Theory of Stochastic Processes II, Grund, math. Wissen., 218, Springer-Verlag, 1975.
[6] B. Grigelionis, On the Markov property of stochastic processes, (in Russian), Lietuvos Mathematikos Rinkinys, 8 (1968), 489-503.
[7] B. Grigelionis, On non-linear filtering theory and absolute continuity of measures corresponding to stochastic processes, Proc. Second Japan-USSR Symp. on Probability Theory, Lecture Notes in Math., 330 (1973), Springer-Verlag, 80-94.
[8] L. Hörmander, Estimates for translation invariant operators in L^p spaces, Acta Math., 104 (1960), 93-140.
[9] T. Komatsu, Markov processes associated with certain integro-differential operators, Osaka J. Math., 10 (1973), 271-303.
[10] T. Komatsu, On the martingale problem for generators of stable processes with perturbations, Osaka J. Math., 21(1984), 113-132.
[11] H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J., 30 (1967), 209-245.
[12] P. Lévy, Théorie de l'Addition des Variables Aléatoires, Gauthier-Villars, Paris, (2^e édition), 1954.
[13] P. A. Meyer, Intégrales stochastiques I, II, Seminaire de Probabilités 1, Université de Strasbourg, Lecture Notes in Math., 39(1967), Springer-Verlag, 72-117.
[14] D. W. Stroock, Diffusion processes associated with Lévy generators, Z. Wahr. Gebiete, 32 (1975), 209-244.
[15] D. W. Stroock and S. R. S. Varadhan, Diffusion processes with continuous coefficients I, II, Comm. Pure Appl. Math., 22 (1969), 345-400, 479-530.
[16] D. W. Stroock and S. R. S. Varadhan, Multidimensional Diffusion Processes, Grund. math. Wissen., 233, Springer-Verlag, 1979.
[17] M. Tsuchiya, On a small drift of Cauchy process, J. Math. Kyoto Univ., 10 (1970), 475-492.
[18] M. Tsuchiya, On some perturbations of stable processes, Proc. Second Japan-USSR Symp. on Probability Theory, Lecture Notes in Math., 330 (1973), Springer-Verlag, 490-497.

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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