Login | Register

Formulae of Beurling-Deny and Lejan For Non-Symmetric Dirichlet Forms


Formulae of Beurling-Deny and Lejan For Non-Symmetric Dirichlet Forms

Hu, Ze-Chun, Ma, Zhe-Ming and Sun, Wei (2006) Formulae of Beurling-Deny and Lejan For Non-Symmetric Dirichlet Forms. Technical Report. Concordia University. Department of Mathematics & Statistics, Montreal, Quebec.

[thumbnail of 2_06_Hu_Ma_Sun.pdf]
Text (application/pdf)
2_06_Hu_Ma_Sun.pdf - Published Version


By the classical Beurling-Deny formula, any regular symmetric Dirichlet form is decomposed into the diffusion, jumping and killing parts. Further, the diffusion part is characterized by LeJan’s formula. In this paper, both the Beurling-Deny formula and LeJan’s formula are extended to regular non-symmetric Dirichlet forms. In addition, a counterexample is presented to show the gap in the Beurling-Deny formula for non-symmetric Dirichlet forms in the existing literatures.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Monograph (Technical Report)
Authors:Hu, Ze-Chun and Ma, Zhe-Ming and Sun, Wei
Series Name:Department of Mathematics & Statistics. Technical Report No.2/06
Corporate Authors:Concordia University. Department of Mathematics & Statistics
Institution:Concordia University
Date:February 2006
Keywords:Beurling-Deny formula, LeJan’s formula, non-symmetric Dirichlet form
ID Code:6673
Deposited On:03 Jun 2010 20:00
Last Modified:18 Jan 2018 17:29


Bertoin J.: Lévy Processes, Cambridge University Press, 1996.

Beurling A. and Deny J.: ‘Dirichlet spaces’, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 208-215.

Bliedtner J.: Dirichlet forms on regular functional spaces, in Seminar on Potential Theory II, Lecture Notes in Math. 226, Springer-Verlag, Berlin-Heidelberg-New York, 1971, 15-62.

Chen Z., Fitzsimmons P.J., Takeda M., Ying J. and Zhang T.: ‘Absolute continuity of symmetric Markov processes’, Ann. Probab. 32 (2004), 2067 - 2098.

Chen Z. and Zhao Z.: ‘Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach’, Proc. Royal Edinburgh 124A (1994), 673-701.

Courant R. and Hilbet D.: Methods of Mathematical Physics, Vol. 1, Wiley (Interscience), New York, 1953.

Ethier S.N. and Kurtz T.G.: Markov Processes: Characterization and Convergence, John Wiley & Sons, 1986.

Fukushima M., Oshima Y. and Takeda M.: Dirichlet Forms and Symmetric Markov Processes, Walter de Gruyter, Berlin-New York, 1994.

Hu Z.C.: Beurling-Deny formula of non-symmetric Dirichlet forms and the theory of semi-Dirichlet forms, Ph.D. Dissertation, Sichuan University, 2004.

Jacob N.: Pseudo-Differential Operators and Markov Processes. Vol. 1: Fourier Analysis and Semigroups, Imperial College Press, London, 2001.

Kim J.H.: ‘Stochastic calculus related to non-symmetric Dirichlet forms’, Osaka J. Math. 24 (1987), 331-371.

Kuwae K.: ‘Functional calculus for Dirichlet forms’, Osaka J. Math. 35 (1998), 683-715.

LeJan Y.: ‘Mesures associ´ees `a une forme de Dirichlet, applications’, Bull. Soc. Math. France 106 (1978), 61-112.

Ma Z.M. and R¨ockner M.: Introduction to the Theory of (Non-Symmetric) Dirichlet Forms, Springer-Verlag, Berlin-Heidelberg-New York, 1992.

Mataloni S.: ‘Representation formulas for non-symmetric Dirichlet forms’, Journal Anal. Appl. 18(4) (1999), 1039-1064.

Mosco U.: ‘Composite media and asymptotic Dirichlet forms’, J. Funct. Anal. 123 (1994),368-421.

Sato K.: L´evy Processes and Infinitely Divisible Distributions, Cambridge University Press, 1999.
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top