Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-27T15:57:24.706Z Has data issue: false hasContentIssue false
  • English
  • Français

Quadratic variation and energy

Published online by Cambridge University Press:  22 January 2016

S. E. Graversen  and
M. Rao
S. E. Graversen
Affiliation:
Department of Mathematics Århus University, Ny Munkegade 8000 Århus C, Denmark
M. Rao
Affiliation:
Department of Mathematics Århus University, Ny Munkegade 8000 Århus C, Denmark
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known that the concept of energy has played a fruitful role in potential theory and Markov processes. Cartan’s work [6] led to kernel-free potential theories of Beurling-Deny [2]. Since then many authors have worked on this, M. Fukushima [8], M. Silverstein [16], J. Bliedner [3], Berg-Forst [1], to name some. In these works, however, the main thrust is Hubert space theoretic.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 100 , December 1985 , pp. 163 - 180
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1985

References

[ 1 ] Berg, C. and Forst, G., Non-symmetric translation invariant Dirichlet forms, Invent. Math., 21 (1973), 199–212.CrossRefGoogle Scholar
[ 2 ] Beurling, A. and Deny, J., Dirichlet spaces, Proc. Nat. Acad. Sci. U.S.A., 45 (1959), 208–215.Google Scholar
[ 3 ] Bliedner, J., Functional spaces and their exceptional sets, Seminar on Potential Theory II, Lecture Notes in Math., 226, Springer, 1971.Google Scholar
[ 4 ] Blumenthal, R. M. and Getoor, R. K., Markov processes and potential theory, Academic Press, 1968.Google Scholar
[ 5 ] Brosamler, G. A., Quadratic variation of potentials and harmonic functions, Trans. Amer. Math. Soc, 149 (1970), 243–257.CrossRefGoogle Scholar
[ 6 ] Cartan, H., Sur les fondements de la théorie du potential, Bull. Soc. Math. France, 691 (1941), 71–96.CrossRefGoogle Scholar
[ 7 ] Dellacherie, C. and Meyer, P. A., Probabilities and Potential, North Holland, 1978.Google Scholar
[ 8 ] Fukushima, M., Dirichlet forms and Markov processes, North Holland/Kodansha, 1980.Google Scholar
[ 9 ] Föllmer, H., Calcul d’ITO sans probabilités, Séminaire de Probabilitiés XV, Lecture Notes in Math., 850, Springer, 1981.Google Scholar
[10] Graversen, S. E. and Rao, M., On a Theorem of Cartan, Preprint Series 33, 1983/84, Aarhus University.Google Scholar
[11] Meyer, P. A., Probability and Potentials, Blaisdell, Massachusetts, 1966.Google Scholar
[12] Meyer, P. A., Un cours sur les intégrates stochastiques, Séminaire de Probabilitiés X, Lecture Notes in Math., Springer, 511 (1976), 245–400.Google Scholar
[13] Meyer, P. A., Le dual de HH1(Rv) Séminaire de Probabilités XI, Lecture Notes in Math., Springer, 581 (1977), 132–195.Google Scholar
[14] Pop-Stōjanovic, Z. R. and Rao, M., Convergence in Energy, Z. Wahrsch. Verw. Gebiete, 69 (1985), 593–608.CrossRefGoogle Scholar
[15] Revuz, D., Mesures associées aux fonctionelles additives de Markov I, Trans. Amer. Math. Soc, 148 (1979), 501–531.Google Scholar
[16] Silverstein, M. L., Symmetric Markov processes, Lecture Notes in Math., 426, Springer, 1974.Google Scholar
[17] Silverstein, M. L., The sector condition implies that semi-polar sets are quasipolar, Z. Wahrsch. Verw. Gebiete, 41 (1977), 13–33.CrossRefGoogle Scholar
[18] Yamada, T. and Oshima, Y., On some representations of continuous additive functionals locally of zero energy, J. Math. Soc. Japan, 36 (1984), 315–339.Google Scholar