Potential operator of a recurrent strong Feller process in the strict sense and boundary value problem

Hisao WATANABE

doi:10.2969/jmsj/01620083

Hisao WATANABE

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JOURNAL FREE ACCESS

1964 Volume 16 Issue 2 Pages 83-95

DOI https://doi.org/10.2969/jmsj/01620083

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Published: 1964 Received: May 06, 1963 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: CITATION Details: Wrong : 1) M. I. Freidlin, Diffusion processes with reflection and a third boundary value problem, Theor. Probability Appl., 8 (1963), 80-88.
2) I. V. Girsanov, Strong Feller processes, I, General properties, Theor. Probability Appl., 5 (1960), 7-28.
3) R. Z. Hasminsky, Ergodic properties of recurrent diffusion processes and stabilizationof the solution to the Cauchy problem for parabolic equation, Theor. Probability Appl., 5 (1960), 196-214.
4) G. A. Hunt, Markov processes and potentials, I, II, III, Illinois J. Math., 1 (1957), 44-93, 1 (1957), 316-369, 2 (1958), 151-213.
5) J. G. Kemeny-J. L. Snell, Potentials for denumerable Markov chains, J. Math. Analysis and Applications, 8 (1960), 196-260.
6) N. Ikeda, On the construction of two dimensional diffusion processes satisfyingWentzell's boundary conditions and its application to boundry value problems, Mem. Coll. Sci. Univ. Kyoto Ser. A, 33 (1961), 368-427.
7) K. Ito, Lectures on the stochastic processes, Tata Inst., Bombay, 1961.
8) S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math. 27 (1957), 55-102.
9) S. Ito, On the Neumann problem for Laplace-Beltrami operators, Proc. Japan Acad., 37 (1961), 267-272.
10) P. A. Meyer, Fonctionelles multiplicatives et additives de Markov, Ann. Inst. Fourier, 12 (1962), 125-230.
11) M. Nagasawa, The adjoint process of a diffusion with reflecting barrier, Kodai Math. Sem. Rep., 13 (1961), 235-248.
12) M. Nagasawa-K. Sato, Some theorems on the time change and killing of Markov processes, to be appeared.
13) K. Sato-H. Tanaka, Local times on the boundary for multi-dimensional reflecting diffusion, Proc. Japan Acad., 38 (1962), 699-702.
14) M. G. Shur, Continuous additive functionals of Markov processes and excessive functions, Dokl. Akad. Nauk SSSR, 137 (1961), 800-803.
15) T. U eno, On recurrent Markov processes, Kodai Math. Sem. Rep., 12 (1960),109-142.
16) T. Ueno, Some limit theorems for temporally discrete Markov processes, J. Facul. Sci. Univ. Tokyo, 7 (1957), 449-462.

Right : [1] M. I. Freidlin, Diffusion processes with reflection and a third boundary value problem, Theor. Probability Appl., 8 (1963), 80-88.
[2] I. V. Girsanov, Strong Feller processes, I, General properties, Theor. Probability Appl., 5 (1960), 7-28.
[3] R. Z. Hasminsky, Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equation, Theor. Probability Appl., 5 (1960), 196-214.
[4] G. A. Hunt, Markov processes and potentials, I, II, III, Illinois J. Math., 1 (1957), 44-93, 1 (1957), 316-369, 2 (1958), 151-213.
[5] J. G. Kemeny-J. L. Snell, Potentials for denumerable Markov chains, J. Math. Analysis and Applications, 8 (1960), 196-260.
[6] N. Ikeda, On the construction of two dimensional diffusion processes satisfying Wentzell's boundary conditions and its application to boundry value problems, Mem. Coll. Sci. Univ. Kyoto Ser. A, 33 (1961), 368-427.
[7] K. Ito, Lectures on the stochastic processes, Tata Inst., Bombay, 1961.
[8] S. Ito, Fundamental solutions of parabolic differential equations and boundary value problems, Japan. J. Math. 27 (1957), 55-102.
[9] S. Ito, On the Neumann problem for Laplace-Beltrami operators, Proc. Japan Acad., 37 (1961), 267-272.
[10] P. A. Meyer, Fonctionelles multiplicatives et additives de Markov, Ann. Inst. Fourier, 12 (1962), 125-230.
[11] M. Nagasawa, The adjoint process of a diffusion with reflecting barrier, Kodai Math. Sem. Rep., 13 (1961), 235-248.
[12] M. Nagasawa-K. Sato, Some theorems on the time change and killing of Markov processes, to be appeared.
[13] K. Sato-H. Tanaka, Local times on the boundary for multi-dimensional reflecting diffusion, Proc. Japan Acad., 38 (1962), 699-702.
[14] M. G. Shur, Continuous additive functionals of Markov processes and excessive functions, Dokl. Akad. Nauk SSSR, 137 (1961), 800-803.
[15] T. U eno, On recurrent Markov processes, Kodai Math. Sem. Rep., 12 (1960), 109-142.
[16] T. Ueno, Some limit theorems for temporally discrete Markov processes, J. Facul. Sci. Univ. Tokyo, 7 (1957), 449-462.

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

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