Polynomials of the occupation field and related random fields

AbstractTo every symmetric Markov process there correspond two random fields over the state space: a Gaussian (“free”) field φx and the occupation field Tx which describes the amount of time spent by a particle at each state. For the Brownian motion in d ⩾ 2 dimensions both fields are generalized. Using a relation between Tx and the field ξx = :φx2:/2 established in a previous publication, polynomials of the fields T and ξ are investigated. In particular, polynomials of T characterize self-intersections of the process