Pseudo-differential operators and Markov processes

Takashi KOMATSU

doi:10.2969/jmsj/03630387

Takashi KOMATSU

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 3 Pages 387-418

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

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Published: 1984 Received: March 04, 1983 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) 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.

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