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Multiple path integrals. (English) Zbl 0604.60075
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)].
Reviewer: J.F.Le Gall

MSC:
60J55 Local time and additive functionals
60J25 Continuous-time Markov processes on general state spaces
60J60 Diffusion processes
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