Open Access
January, 1994 Decomposition of Dirichlet Processes and its Application
T. J. Lyons, T. S. Zhang
Ann. Probab. 22(1): 494-524 (January, 1994). DOI: 10.1214/aop/1176988870


We extend the forward-backward martingale approach to Stratonovich integrals developed by Zheng and Lyons to the general context of Dirichlet spaces. From this perspective, it is clear that the Stratonovich integral of an $L^2$ 1-form against a Dirichlet process is well defined, coordinate invariant, and obeys appropriate chain rules. The paper continues by examining the tightness and continuity of the mapping from Dirichlet forms to probability measures on path space. Some positive results are obtained for a class of infinite-dimensional diffusions.


Download Citation

T. J. Lyons. T. S. Zhang. "Decomposition of Dirichlet Processes and its Application." Ann. Probab. 22 (1) 494 - 524, January, 1994.


Published: January, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0804.60044
MathSciNet: MR1258888
Digital Object Identifier: 10.1214/aop/1176988870

Primary: 60J45
Secondary: 31C25 , 60B11 , 60B12 , 60J35

Keywords: Dirichlet processes , Dirichlet spaces , Stratonovich integral , tightness

Rights: Copyright © 1994 Institute of Mathematical Statistics

Vol.22 • No. 1 • January, 1994
Back to Top