Functional Central Limit Theorem for Additive Functionals Associated to the Generalized Nelson Hamiltonian

Abstract

In this paper, we give a generalization of the Nelson Hamiltonian. Then, by computing explicitly the diffusion constant, we prove a functional central limit theorem (FCLT) for additive functionals associated with this Hamiltonian. This result recovers the classical and the relativistic cases. Finally a fractional version of this FCLT is given.Received 2018-10-28; Communicated by the editors. 2010 Mathematics Subject Classification. Primary 47D07, 47D08; Secondary 60J75, 81Q10.