Superposition of diffusion processes

Matsuyo TOMISAKI

doi:10.2969/jmsj/03240671

Matsuyo TOMISAKI

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 4 Pages 671-696

DOI https://doi.org/10.2969/jmsj/03240671

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Published: 1980 Received: January 17, 1979 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) R.A. Adams, Sobolev spaces, Academic press, New York and London, 1975.
2) N. Aronsjazn and K. T. Smith, Theory of Bessel potentials, Part I, Ann. Inst. Fourier (Grenoble), 11 (1961), 385-475.
3) R.M. Blumenthal and R.K. Getoor, Markov processes and Potential Theory, Academic press, New York and London, 1968.
4) P. Courrége and P. Priouret, Recollements de processus de Markov continus, C. R. Acad. Sci. Paris, 259 (1964), 4220-4222.
5) M. Fukushima, Local property of Dirichlet forms and continuity of sample paths, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 29 (1974), 1-6.
6) M. Fukushima, Potential theory of symmetric Markov processes and its applications, Proc. 3rd Japan-USSR symp. on probability theory, Lecture Notes in Math., vol. 550, Springer-Verlag, Berlin-Heidelberg-New York, 1976.
7) M. Fukushima, Dirichlet forms and Markov processes, Kodansha, Tokyo, 1980.
8) E. De Giorgi, Sulla differenziabilità e l'analicità della estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Fis Mat. Natur., Ser. 3, 3 (1957), 25-43.
9) M. M. Hamza, Détermination des formes de Dirichlet sur Rⁿ, Thèse de 3 ème cycle, Orsay, 1975.
10) N. Ikeda and S. Watanabe, The local structure of a class of diffusions and related problems, Proc. 2nd Japan-USSR symp. on probability theory, Lecture Notes in Math., vol. 330, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
11) M. Kanda, Regular points and Green functions in Markov processes, J. Math. Soc. Japan, 19 (1967), 46-69.
12) H. Kunita, General boundary conditions for multi-dimensional diffusion processes, J. Math. Kyoto Univ., 10 (1970), 273-335.
13) J. Moser, A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., 13 (1960), 457-468.
14) J. Nash, Parabolic equations, Proc. Nat. Acad. Sci. U.S.A., 43 (1957), 754-758.
15) L. Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., 8 (1955), 648-674.
16) G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montréal, 1966.

Right : [1] R. A. Adams, Sobolev spaces, Academic press, New York and London, 1975.
[2] N. Aronsjazn and K. T. Smith, Theory of Bessel potentials, Part I, Ann. Inst. Fourier (Grenoble), 11 (1961), 385-475.
[3] R. M. Blumenthal and R. K. Getoor, Markov processes and Potential Theory, Academic press, New York and London, 1968.
[4] P. Courrége and P. Priouret, Recollements de processus de Markov continus, C. R. Acad. Sci. Paris, 259 (1964), 4220-4222.
[5] M. Fukushima, Local property of Dirichlet forms and continuity of sample paths, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 29 (1974), 1-6.
[6] M. Fukushima, Potential theory of symmetric Markov processes and its applications, Proc. 3rd Japan-USSR symp. on probability theory, Lecture Notes in Math., vol. 550, Springer-Verlag, Berlin-Heidelberg-New York, 1976.
[7] M. Fukushima, Dirichlet forms and Markov processes, Kodansha, Tokyo, 1980.
[8] E. De Giorgi, Sulla differenziabilità e l'analicità della estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino Cl. Fis Mat. Natur., Ser. 3, 3 (1957), 25-43.
[9] M. M. Hamza, Détermination des formes de Dirichlet sur Rⁿ, Thèse de 3 ème cycle, Orsay, 1975.
[10] N. Ikeda and S. Watanabe, The local structure of a class of diffusions and related problems, Proc. 2nd Japan-USSR symp. on probability theory, Lecture Notes in Math., vol. 330, Springer-Verlag, Berlin-Heidelberg-New York, 1973.
[11] M. Kanda, Regular points and Green functions in Markov processes, J. Math. Soc. Japan, 19 (1967), 46-69.
[12] H. Kunita, General boundary conditions for multi-dimensional diffusion processes, J. Math. Kyoto Univ., 10 (1970), 273-335.
[13] J. Moser, A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations, Comm. Pure Appl. Math., 13 (1960), 457-468.
[14] J. Nash, Parabolic equations, Proc. Nat. Acad. Sci. U. S. A., 43 (1957), 754-758.
[15] L. Nirenberg, Remarks on strongly elliptic partial differential equations, Comm. Pure Appl. Math., 8 (1955), 648-674.
[16] G. Stampacchia, Équations elliptiques du second ordre à coefficients discontinus, Les Presses de l'Université de Montréal, 1966.

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