A representation for functionals of superprocesses via particle picture

Super-Brownian Local Time: a Representation and Two Applications

“…The following theorem, together with Proposition 2.3 in [7], implies that the three notions of super-Brownian local time referred to in the introductory section yield equivalent concepts.…”

“…In [7], Feldman and Iyer proved that the local times L t and l t are equivalent concepts. In this note, we use a semimartingale representation of local time (Theorem 3.1) to show that the three notions of local time L t , l t , and L t are equivalent.…”

Existence of self-intersection local time of the multitype Dawson-Watanabe superprocess

“…Let χ 1 denote the space of equivalence classes of χ 0 1 modulo (•, •) 1 . There exist a unique isometry (which we again denote by) I 1 from χ 1 to L 2 1 obeying (1.4). Moreover, for every ϕ ∈ χ 0 1 , the process M ϕ t := I 1 (ϕ) = ϕ(x, s)1 s≤t dZ x,s is a martingale, and every L 2 1 -valued martingale can be represented in this form.…”