HIERARCHY OF LÉVY–LAPLACIANS AND QUANTUM STOCHASTIC PROCESSES

Abstract

We consider a family of infinite dimensional Laplace operators which contains the classical Lévy–Laplacian. We prove a representation of these operators as a quadratic functions of quantum stochastic processes. Particularly, for the classical Lévy–Laplacian, the following formula is proved: ΔL = lim ε→0 ∫‖s-t‖<ε bsbtdsdt, where bt is the annihilation process.