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On the Singularity of Green functions in Markov Processes

Published online by Cambridge University Press:  22 January 2016

Mamoru Kanda
Mamoru Kanda*
Affiliation:
Nagoya University
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In the previous paper [6] we have discussed Markov processes in Rd with the Green function G (x, y) satisfying are positive constants), and showed that the regular points of its process are the same as those of α-stable process. The present article is closely related to the previous one.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 33 , November 1968, pp. 21 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Deny, J., Le Balayage, Meddel. Lunds Univ. Mat. Sem., tome dedié à M. Riesz (1952), 47–61.Google Scholar
[2] Dynkin, E.B., Markov process, Springer-Verlag, Berlin.Google Scholar
[3] Frostman, O., Potentiel d’equilibre et capacité des ensembles avec quelques applications à la theorie des fonctions, Meddel. Lunds Univ. Mat. Sem. 3 (1935).Google Scholar
[4] Hunt, G.A., Mrkoff processes and potentials. 3, Illinois J. Math. (1958), 151–213.Google Scholar
[5] Ito, K. and Mckean, H.P. Jr, Diffusion processes and their sample paths, Springer-Verlag, 1965.Google Scholar
[6] Kanda, M., Regular points and Green functions in Markov processes, J. Math. Soc. Japan, Vol. 19, No. 1, (1967), 46–69.Google Scholar
[7] Kanda, M., A remark on the continuity of the dual process, Nagoya Math. J. Vol. 32, (1968), 287–295.CrossRefGoogle Scholar
[8] Krylov, N.V., On quasi-diffusional processes, Theorey Probability Appl. (USSR) (1966), 424–443.Google Scholar
[9] Krylov, N.V., On the green function for the Dirichlet problem, Uspehi Mat. Nauk, Tom. 22. No. 2 (134) (1967), 116–118.Google Scholar
[10] Kunita, H. and Watanabe, T., Markov processes and Martin boundaries, Illinois J. Math., 9 (1965), 485–526.Google Scholar
[11] Meyer, P.A., Proprietes des fonctions excessives, Séminaire Brelot-Choquet-Deny (théorie du potentiel), (1960-1961).Google Scholar
[12] Meyer, P.A., Semi-groupes en dualité, Séminaire Brelot-Choquet-Deny (théorie du potentiel), (1960-1961).Google Scholar
[13] Meyer, P.A., Fonctionelles multiplicatives et additives de Markov, Ann. Inst. Fourier, 12 (1962).Google Scholar
[14] Sur, M.G., Martin boundary for linear elliptic operators of second order, Izv. Akad. Nauk (USSR), 27 (1963), 45–60.Google Scholar
[15] Watanabe, S., Takeuchi, J. and Yamada, T., Stable process, Sem. on Prob. Vol. 13, (in Japanese).Google Scholar
[16] Kametani, S., On Hausdorff’s measures and generalized capacities with some of their applications to the theory of functions. Japanese J. Math. 19 (1944), 217–257.Google Scholar
[17] Taylor, S.J., On the connection between Hausdorff measures and generalized capasity. Proc. Cambridge Philos. Soc., 57 (1961), 524–531.Google Scholar