Abstract
LetB be a separable real Banach space andX(t) be a symmetric conservative diffusion process taking values inB. In this paper, we decompose the functionalu(X(t),t) into a sum of a square integrable martingale and a regular 0-quadratic variation process. On this basis, we establish the predictable representation theorem ofX(t).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
T. Lyons and W.A. Zheng, Diffusion Processes with Non-smooth Diffusion Coefficients and Their Density Functions, Preprint.
Fan Ru-zong, Decomposition of a Class of Functionals,Acta Mathematicae Sinica (English Series),7:3(1991), 224–240.
M., Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Publishing Company, 1980.
Fan Ru-zong, Representation of Martingale Additive Functionals On Banach Spaces,Acta Mathematicae Applicatae Sinica (English Series),6:1(1990), 74–80.
W.A. Zheng, On Representation Theorem of Diffusion Processes with Non-smooth Diffusion Coefficients, Preprint.
Author information
Authors and Affiliations
Additional information
This project is supported by the National Natural Science Foundation of China.
Rights and permissions
About this article
Cite this article
Fan, R. Decomposition of a class of functionals and the predictable representation theorem on Banach spaces. Acta Mathematicae Applicatae Sinica 8, 153–167 (1992). https://doi.org/10.1007/BF02006151
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02006151