On stable processes with boundary conditions

Shinzo WATANABE

doi:10.2969/jmsj/01420170

Shinzo WATANABE

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1962 Volume 14 Issue 2 Pages 170-198

DOI https://doi.org/10.2969/jmsj/01420170

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Published: 1962 Received: August 31, 1961 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: AFFILIATION Details: Wrong :
1) University of Tyoto

Right :
1) University of Kyoto

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. M. Blumenthal and R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc., 95 (1960), 263-273.
2) J. Elliott, The boundary value problems and semi-groups associated with certain integro-differential operators, Trans. Amer. Math. Soc., 76 (1954), 300-331.
3) J. Elliott, Absorbing barrier processes connected with the symmetric stable densities, Illinois J. Math., 3 (1959), 200-216.
4) G. A. Hunt, Some theorems concerning Brownian motion, Trans. Amer. Math. Soc., 81 (1956), 294-319.
5) G. A. Hunt, Markov processes and potentials, Illinois J. Math., 1 (1957), 44-93.
6) N. Ikeda, T. Ueno, H. Tanaka and K. Sato, On the boundary problems of multidimensional diffusions (Japanese), Seminar on Prob., vol. 6.
7) K. Ito, Stochastic process, Tata Institute notes, to appear.
8) K. Ito and H. P. McKean, Diffusion, to appear.
9) M. Kac, On some connections between probability theory and differential and integral equations, Proceedings of the second Berkeley symposium, Berkeley, 1950, 189-215.
10) H. P. McKean, Sample functions of stable processes, Annals of Math., 61 (1955), 564-579.
11) G. Pólya and G. Szegö, Über den transfiniten Durchmesser (Kapzitätskonstante) von ebenen und räumlichen Punktmengen, J. Reine Angew. Math., 165 (1931), 4-49.
12) D. Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc. 87 (1958), 187-197.
13) F. G. Tricomi, Integral equations, New York, 1957.
14) H. Widom, Stable processes and integral equations, Trans. Amer. Math. Soc., 98 (1961), 430-448.

Right : [1] R. M. Blumenthal and R. K. Getoor, Some theorems on stable processes, Trans. Amer. Math. Soc., 95 (1960), 263-273.
[2] J. Elliott, The boundary value problems and semi-groups associated with certain integro-differential operators, Trans. Amer. Math. Soc., 76 (1954), 300-331.
[3] J. Elliott, Absorbing barrier processes connected with the symmetric stable densities, Illinois J. Math., 3 (1959), 200-216.
[4] G. A. Hunt, Some theorems concerning Brownian motion, Trans. Amer. Math. Soc., 81 (1956), 294-319.
[5] G. A. Hunt, Markov processes and potentials, Illinois J. Math., 1 (1957), 44-93.
[6] N. Ikeda, T. Ueno, H. Tanaka and K. Sato, On the boundary problems of multidimensional diffusions (Japanese), Seminar on Prob., vol. 6.
[7] K. Ito, Stochastic process, Tata Institute notes, to appear.
[8] K. Ito and H. P. McKean, Diffusion, to appear.
[9] M. Kac, On some connections between probability theory and differential and integral equations, Proceedings of the second Berkeley symposium, Berkeley, 1950, 189-215.
[10] H. P. McKean, Sample functions of stable processes, Annals of Math., 61 (1955), 564-579.
[11] G. Pólya and G. Szegö, Über den transfiniten Durchmesser (Kapzitätskonstante) von ebenen und räumlichen Punktmengen, J. Reine Angew. Math., 165 (1931), 4-49.
[12] D. Ray, Stable processes with an absorbing barrier, Trans. Amer. Math. Soc. 87 (1958), 187-197.
[13] F. G. Tricomi, Integral equations, New York, 1957.
[14] H. Widom, Stable processes and integral equations, Trans. Amer. Math. Soc., 98 (1961), 430-448.

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

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