Resumen de Permanental fields, loop soups and continuous additive functionals
Yves Le Jan, Michael B. Marcus, Jay Rosen
A permanental field, ψ={ψ(ν),ν∈V}, is a particular stochastic process indexed by a space of measures on a set S. It is determined by a kernel u(x,y), x,y∈S, that need not be symmetric and is allowed to be infinite on the diagonal. We show that these fields exist when u(x,y) is a potential density of a transient Markov process X in S.
A permanental field ψ can be realized as the limit of a renormalized sum of continuous additive functionals determined by a loop soup of X, which we carefully construct. A Dynkin-type isomorphism theorem is obtained that relates ψ to continuous additive functionals of X (continuous in t), L={Lνt,(ν,t)∈V×R+}. Sufficient conditions are obtained for the continuity of L on V×R+. The metric on V is given by a proper norm.
