On the generation of Markov processes by symmetric forms

A. Beurling and J. Deny: Dirichlet spaces, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 208–215.
Article MathSciNet MATH Google Scholar
R.M. Blumenthal and R.K. Getoor: Markov processes and potential theory, Academic Press, New York and London, 1968.
MATH Google Scholar
J. Deny: Méthodes Hilbertiennes en théorie du potentiel, Potential Theory, Centro Internazionale Matematico Estivo, Edizioni Cremonese, Roma, 1970, pp. 121–201.
MATH Google Scholar
J. Deny-J.L. Lions: Les espaces du type de Beppo Levi, Ann. Inst. Fourier (Grenoble) 5 (1953/54), 305–370.
Article MathSciNet MATH Google Scholar
E.B. Dynkin: Markov processes, Springer-Verlag, Berlin, 1965.
Book MATH Google Scholar
J. Elliott: Dirichlet spaces and boundary conditions for submarkovian resolvents, J. Math. Anay. Appl. 36 (1971), 251–282.
Article MathSciNet MATH Google Scholar
J. Elliott and M.L. Silverstein: On boundary conditions for symmetric submarkovian resolvents, Bull. Amer. Math. Soc. 76 (1970), 752–757.
Article MathSciNet MATH Google Scholar
M. Fukushima: On boundary conditions for multi-dimensional Brownian motions with symmetric resolvent densities, J. Math. Soc. Japan 21 (1969), 58–93.
Article MathSciNet MATH Google Scholar
M. Fukushima: Regular representations of Dirichlet spaces, Trans. Amer. Math. Soc. 155 (1971), 455–473.
Article MathSciNet MATH Google Scholar
M. Fukushima: Dirichlet spaces and strong Markov processes, Trans. Amer. Math. Soc. 162 (1971), 185–224.
Article MathSciNet MATH Google Scholar
N. Ikeda and S. Watanabe: The local structure of a class of diffusions and related problems, Proceedings of the Second Japan — USSR Symposium on Probability Theory.
Google Scholar
T. Kato: Perturbation theory for linear operators, Springer-Verlag, Berlin, 1966.
Book MATH Google Scholar
M.G. Krein: The theory of self-adjoint extensions of semibounded Hermitian transformations and its applications, Mat. Sbornik 20 (1947), 431–495 (Russian).
MathSciNet MATH Google Scholar
P.A. Meyer: Probability and Potentials, Ginn, Blaisdell, Waltham, Mass., 1966.
MATH Google Scholar
P.A. Meyer: Processus de Markov, Lecture Notes in Math., no. 26, Springer-Verlag, Berlin, 1967.
MATH Google Scholar
M.L. Silverstein: Dirichlet spaces and random time change, to appear.
Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics, Osaka University, Toyonaka, Japan
Masatoshi Fukushima

Authors

Masatoshi Fukushima
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

G. Maruyama Yu. V. Prokhorov

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Fukushima, M. (1973). On the generation of Markov processes by symmetric forms. In: Maruyama, G., Prokhorov, Y.V. (eds) Proceedings of the Second Japan-USSR Symposium on Probability Theory. Lecture Notes in Mathematics, vol 330. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061480

Download citation

DOI: https://doi.org/10.1007/BFb0061480
Published: 24 August 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-06358-2
Online ISBN: 978-3-540-46956-8
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

On the generation of Markov processes by symmetric forms

Access this chapter

Preview

References