Keywords
- Dirichlet Form
- Finite Energy
- Excessive Function
- Strong Markov Property
- Brownian Motion Process
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Beurling, A., and Deny, J., Espaces de Dirichlet I. Le cas elementaire, Acta Math. 99,3–4 (1958).
Blumenthal, R.M., and Getoor, R.K., Markov processes and their potential theory, Academic Press, New York (1968).
Bliedtner, J., Functional spaces and their exceptional sets, Seminar on Potential Theory II Lecture Notes in Math., 226, Springer-Verlag, Berlin-Heidelberg-New York, (1971).
Cartan, H., Sur les fondaments de la theorie du potentiel, Bull. Soc.Math.France, 69,71–96 (1941).
Cartan, H., Theorie du potentiel newtonian: energie, capacite, suites de potentiels, Bull.Soc.Math.France, 73, 74–106 (1945).
Deny, J., Sur les infinis d'un potentiel, C.R.Acad.Sci.Paris, 224,524–525 (1947).
Deny, J., Les potentiels d'energie finie, Acta Math., 82, 107–183 (1950).
Doob, J.L., Classical Potential Theory and its Probabilistic Counterpart, Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, (1984).
Feller,W., An Introduction to Probability Theory and Its Applications, Vol.II, Second Edition, Wiley, (1970).
Forst, G., A characterization of non-symmetric translation invariant Dirichlet forms, Theorie du potentiel et analyse harmonique, Lecture Notes in Math., 404, 113–125, Springer Verlag (1974).
Fukushima, M., Dirichlet Forms and Markov Processes, North-Holland/ Kodansha (1980).
Gauss,C.F., Allgemeine Lehrsatze in Beziehung auf die im verkehztem Verhaltnisse des Quadrats der Entfernung wizkende Anziehungs — und Abstossangskraffe, Leipzig (1840).
Glover, J., Energy and Maximum Principle for nonsymmetric Hunt Processes, Probability Theory and its Applications, XXVI,4, 757–768, Moscow, (1981).
Glover, J., and Rao,Murali, Hunt's Hypothesis (H) and Getoor's Conjecture, Annals of Probability, (to appear).
Hawkes, J., Potential Theory of Levy processes, Proc. of London Math.Soc., 38, 335–352, (1979).
Helms, L.L., Introduction to Potential Theory, Wiley (1969).
Hunt, G.A., Markoff Processes and Potentials, Illinois Journal of Mathematics, Vol. I, 44–93, (1957).
Hunt, G.A., Markoff Processes and Potentials, Illinois Journal of Mathematics, vol.I, 316–369, (1957).
Hunt, G.A., Markoff Processes and Potentials, Illinois Journal of Mathematics, vol.II, 151–213, (1958).
Ito, K., and McKean, H.P., Jr. Diffusion Processes and their simple Paths, Springer-Verlag, New York, Berlin, Heidelberg, (1965).
Kanda, M., Two theorems on capacity for Markov processes with independent increments, Z.W. und V.Gebiete, 35,159–166 (1976).
Kesten,H., Hitting probabilities of single points for processes with stationary independent increments, Memoirs of the AMS, 93, (1969).
Meyer, P.A., Probability and Potentials, Blaisdell, (1966).
Pop-Stojanović, Z.R.,Rao, Murali, Some results on Energy, Seminar on Stohastic Processes 1981, 135–150, Boston, Birkhauser (1981).
Pop-Stojanović, Z.R.,Rao, Murali, Remarks on Energy, Seminar on Stohastic Processes 1982, 229–237, Boston, Birkhauser (1983).
Pop-Stojanović, Z.R., Rao, Murali, Further Results on Energy, Seminar on Stohastic Processes 1983, 143–150, Boston, Birkhauser, (1984).
Pop-Stojanović, Z.R.,Rao, Murali, Convergence in Energy, Z.W. und V.Gebiete, 69, 593–608, (1985).
Port, S., and Stone, C., Brownian Motion and Classical Potential Theory, Academic Press, New York (1978).
Rao, Murali, Brownian Motion and Classical Potential Theory, Aarhus University, Lecture Notes Series, No.47 (1977).
Rao, Murali, On a result of M.Kanda, Z.W. und V.Gebiete, 41, 35–37 (1977).
Rao, Murali, A note on Revuz measure, Seminaire de probabilites XIV, 1978/79, Lecture Notes in Mathematics 784, 1980, 418–436.
Rao, Murali, Representation of excessive functions, Math. Scand. 51, 367–381,(1982).
Revuz, D., Measures associees a functionnelles additives de Markov I, Trans.Am.Math.Soc., 148, 501–531,(1970).
Silverstein, M.L., The sector condition implies that semipolar sets are quasi-polar, Z.W.verw.Gebiete, 41, 13–33,(1977).
Weil, M., Quasi-processus et energie, Seminaire de probabilities V Lecture Notes 191, 347–361, Berlin-Heidelberg-New York, Springer, (1971).
Wiener, N., The Dirichlet Problem, J.Math.Phys. 3, 127–146,(1924).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this chapter
Cite this chapter
Pop-Stojanović, Z.R. (1987). Energy in Markov processes. In: Butković, D., Kurepa, S., Kraljević, H. (eds) Functional Analysis II. Lecture Notes in Mathematics, vol 1242. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072445
Download citation
DOI: https://doi.org/10.1007/BFb0072445
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17833-0
Online ISBN: 978-3-540-47876-8
eBook Packages: Springer Book Archive
