Intersection local times in L2 for Markov processess
Alexey RudenkoTheory of Stochastic Processes
Vol.24 (40), no.1, 2019, pp.64-95
We provide sufficient conditions for the existence of intersection and self-intersection local times with additional weight in the space of square integrable random variables for Markov processes under specific local upper bounds for their transition density. We determine when this condition is satisfied for standard Brownian motion, symmetric stable processes and Brownian motions on Carnot group.