Generalized Kac's moment formula for positive continuous additive functionals of Markov processes
Abstract
We establish a formula for moments of certain random variables involving positive continuous additive functionals (PCAFs) of standard processes which have absolutely continuous transition functions and are in duality with standard processes with absolutely continuous transition functions,generalizing the classical Kac's moment formula. In particular, all our results are applicable to the more familiar case of symmetric Hunt processes which are associated with regular Dirichlet forms and have absolutely continuous transition functions.
Cite
@article{arxiv.2503.04210,
title = {Generalized Kac's moment formula for positive continuous additive functionals of Markov processes},
author = {Naotaka Kajino and Ryoichiro Noda},
journal= {arXiv preprint arXiv:2503.04210},
year = {2026}
}
Comments
14 pages, A new section (Section 4) has been added, extending the results from symmetric Hunt processes to a broader class of standard Markov processes admitting a dual process. The proofs have been revised to avoid the use of symmetric Dirichlet form theory. The title has been modified accordingly