Multiple path integrals
The notion of additive functional of order k for a Markov process is introduced and studied in a general setting. Usual additive functionals are recovered in the case \(k=1\). An important special case of these generalized additive functionals is the self-intersection local times of Brownian motion, which have been studied in many recent papers. A relationship is described between additive functionals of order k for one process, and additive functionals of k independent processes, which have been studied by the author in a previous paper [J. Funct. Anal. 42, 64- 101 (1981; Zbl 0467.60069)].
self-intersection local times of Brownian motion
scientific article; zbMATH DE number 3976041
scientific article