On some representations of continuous additive functionals locally of zero energy

Yôichi ÔSHIMA; Toshio YAMADA

doi:10.2969/jmsj/03620315

Yôichi ÔSHIMA, Toshio YAMADA

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JOURNAL FREE ACCESS

1984 Volume 36 Issue 2 Pages 315-339

DOI https://doi.org/10.2969/jmsj/03620315

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Published: 1984 Received: May 26, 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: AUTHOR Details: Wrong : Yoichi OSHIMA¹⁾, Toshio YAMADA²⁾
Right : Yôichi ÔSHIMA¹⁾, Toshio YAMADA²⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Academic Press, New York-London, 1968.
2) M. Fukushima, A decomposition of additive functionals of finite energy, Nagoya Math. J., 74 (1979), 137-168.
3) M. Fukushima, Dirichlet forms and Markov processes, Kodansha - North Holland, Tokyo-Amsterdam-Oxford-New York, 1980.
4) M. Fukushima, On a representation of local martingale additive functionals of symmetric diffusions, Lecture Notes in Math., 851, Springer-Verlag, 1981.
5) M. Fukushima, On absolute continuity of multidimensional symmetrisable diffusions, Lecture Notes in Math., 923, Springer-Verlag, 1982.
6) M. Hasegawa and H. Tanaka, Stochastic differential equations, 19, Seminar on Prob. (in Japanese), 1964.
7) N. Ikeda and S. Manabe, Integral of differential forms along the path of diffusion processes, Publ. RIMS Kyoto Univ., 15 (1979), 827-852.
8) K. Ito and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
9) H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J., 30 (1967), 209-245.
10) H. P. McKean, Jr., Stochastic integrals, Academic Press, New York-London, 1969.
11) H. P. McKean, Jr. and H. Tanaka, Additive functionals of the Brownian path, Mem. Coll. Sci. Univ. Kyoto Ser. A Math., 33 (1961), 476-506.
12) P. A. Meyer, Un cours sur les intégrales stochastiques, Lecture Notes in Math., 511, Springer-Verlag, 1976.
13) M. Motoo and S. Watanabe, On a class of additive functionals of Markov processes, J. Math. Kyoto Univ., 4 (1965), 429-469.
14) D. Revuz, Mesures associées aux fonctionelles additives de Markov I, Trans. Amer. Math. Soc., 148 (1970), 501-531.
15) M. L. Silverstein, Symmetric Markov processes, Lecture Notes in Math., 426, Springer-Verlag, 1974.
16) H. Tanaka, Note on continuous additive functionals of the 1-dimensional Brownian path, Z. Wahr., 1 (1963), 251-257.
17) A. D. Ventcel, Non-negative additive functionals of Markov processes, Soviet Math. Dokl. (English translation of Dokl. Acad. Nauk SSSR), 2 (1961), 218-221.
18) J. B. Walsh, Markov processes and their functionals in duality, Z. Wahr., 24 (1972), 229-246.
19) T. Yamada, On some representations concerning the stochastic integrals, to appear in Prob. Math. Stat., 4.
20) Ch. Yoeurp, Une decomposition multiplicative de la valeur absolue d'un mouvement Brownien, Lecture Notes in Math., 920, Springer-Verlag, 1982, 234-237.
21) M. Yor, Sur la transformée de Hilbert des temps locaux Browniens et une extension de la formule d'Ito, Lecture Notes in Math., 238-247.

Right : [1] R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Academic Press, New York-London, 1968.
[2] M. Fukushima, A decomposition of additive functionals of finite energy, Nagoya Math. J., 74 (1979), 137-168.
[3] M. Fukushima, Dirichlet forms and Markov processes, Kodansha - North Holland, Tokyo-Amsterdam-Oxford-New York, 1980.
[4] M. Fukushima, On a representation of local martingale additive functionals of symmetric diffusions, Lecture Notes in Math., 851, Springer-Verlag, 1981.
[5] M. Fukushima, On absolute continuity of multidimensional symmetrisable diffusions, Lecture Notes in Math., 923, Springer-Verlag, 1982.
[6] M. Hasegawa and H. Tanaka, Stochastic differential equations, 19, Seminar on Prob. (in Japanese), 1964.
[7] N. Ikeda and S. Manabe, Integral of differential forms along the path of diffusion processes, Publ. RIMS Kyoto Univ., 15 (1979), 827-852.
[8] K. Itô and H. P. McKean, Jr., Diffusion processes and their sample paths, Springer-Verlag, Berlin-Heidelberg-New York, 1965.
[9] H. Kunita and S. Watanabe, On square integrable martingales, Nagoya Math. J., 30 (1967), 209-245.
[10] H. P. McKean, Jr., Stochastic integrals, Academic Press, New York-London, 1969.
[11] H. P. McKean, Jr. and H. Tanaka, Additive functionals of the Brownian path, Mem. Coll. Sci. Univ. Kyoto Ser. A Math., 33 (1961), 476-506.
[12] P. A. Meyer, Un cours sur les intégrales stochastiques, Lecture Notes in Math., 511, Springer-Verlag, 1976.
[13] M. Motoo and S. Watanabe, On a class of additive functionals of Markov processes, J. Math. Kyoto Univ., 4 (1965), 429-469.
[14] D. Revuz, Mesures associées aux fonctionelles additives de Markov I, Trans. Amer. Math. Soc., 148 (1970), 501-531.
[15] M. L. Silverstein, Symmetric Markov processes, Lecture Notes in Math., 426, Springer-Verlag, 1974.
[16] H. Tanaka, Note on continuous additive functionals of the 1-dimensional Brownian path, Z. Wahr., 1 (1963), 251-257.
[17] A. D. Ventcel, Non-negative additive functionals of Markov processes, Soviet Math. Dokl. (English translation of Dokl. Acad. Nauk SSSR), 2 (1961), 218-221.
[18] J. B. Walsh, Markov processes and their functionals in duality, Z. Wahr., 24 (1972), 229-246.
[19] T. Yamada, On some representations concerning the stochastic integrals, to appear in Prob. Math. Stat., 4.
[20] Ch. Yoeurp, Une decomposition multiplicative de la valeur absolue d'un mouvement Brownien, Lecture Notes in Math., 920, Springer-Verlag, 1982, 234-237.
[21] M. Yor, Sur la transformée de Hilbert des temps locaux Browniens et une extension de la formule d'Itô, Lecture Notes in Math., 920, Springer-Verlag, 1982, 238-247.

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