On Nelson processes with boundary condition

Minoru YOSHIDA

doi:10.2969/jmsj/04220193

Minoru YOSHIDA

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JOURNAL FREE ACCESS

1990 Volume 42 Issue 2 Pages 193-212

DOI https://doi.org/10.2969/jmsj/04220193

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Published: 1990 Received: August 04, 1988 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) E. A. Carlen, Conservative diffusions, Comm. Math. Phys., 94 (1984), 293-315.
2) E. A. Carlen, Existence and sample path properties of the diffusions in Nelson's stochastic mechanics, Lecture Notes in Math., 1158, Springer, 1984, pp. 25-51.
3) C. Dellacherie and P.A. Meyer, Probability and potential, North-Holland, Amsterdam, 1978.
4) C. Dellacherie and P.A. Meyer, Probability and potential B, North-Holland, Amsterdam, 1982.
5) S. Ito, Fundamental solution of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
6) S. Ito, Functional analysis III, Kisosugaku, Iwanami shyoten, Tokyo, 1978 (in Japanese).
7) Y. Kannai, Existence and smoothness for certain degenerate parabolic boundary value problems, Osaka J. Math., 25 (1988), 1-18.
8) P. A. Meyer and W. A. Zheng, Construction de processus de Nelson reversibles, Lecture Notes in Math., 1123, Springer, 1983/1984, pp. 12-26.
9) M. Nagasawa, Transformation of diffusion and Shrödinger processes, Report at UCSD in 1987.
10) E. Nelson, Derivation of Schrödinger equation from Newtonian mechanics, Phys. Rev., 150 (1966), 1079-1085.
11) D. W. Stroock and S. R. S. Varadhan, Diffusion processes with boundary conditions, Commun. Pure Appl. Math., 24 (1971), 147-225.
12) S. Watanabe, Stochastic differential equations, Sangyo-toshyo, Tokyo, 1975 (in Japanese).

Right : [1] E. A. Carlen, Conservative diffusions, Comm. Math. Phys., 94 (1984), 293-315.
[2] E. A. Carlen, Existence and sample path properties of the diffusions in Nelson's stochastic mechanics, Lecture Notes in Math., 1158, Springer, 1984, pp. 25-51.
[3] C. Dellacherie and P. A. Meyer, Probability and potential, North-Holland, Amsterdam, 1978.
[4] C. Dellacherie and P. A. Meyer, Probability and potential B, North-Holland, Amsterdam, 1982.
[5] S. Itô, Fundamental solution of parabolic differential equations and boundary value problems, Japan. J. Math., 27 (1957), 55-102.
[6] S. Itô, Functional analysis III, Kisosugaku, Iwanami shyoten, Tokyo, 1978 (in Japanese).
[7] Y. Kannai, Existence and smoothness for certain degenerate parabolic boundary value problems, Osaka J. Math., 25 (1988), 1-18.
[8] P. A. Meyer and W. A. Zheng, Construction de processus de Nelson reversibles, Lecture Notes in Math., 1123, Springer, 1983/1984, pp. 12-26.
[9] M. Nagasawa, Transformation of diffusion and Shrödinger processes, Report at UCSD in 1987.
[10] E. Nelson, Derivation of Schrödinger equation from Newtonian mechanics, Phys. Rev., 150 (1966), 1079-1085.
[11] D. W. Stroock and S. R. S. Varadhan, Diffusion processes with boundary conditions, Commun. Pure Appl. Math., 24 (1971), 147-225.
[12] S. Watanabe, Stochastic differential equations, Sangyo-toshyo, Tokyo, 1975 (in Japanese).

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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