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HIERARCHY OF LÉVY–LAPLACIANS AND QUANTUM STOCHASTIC PROCESSES

BORIS O. VOLKOV

Department of Mechanics and Mathematics, Moscow State University, Leninskie Gory 1, Moscow, 119991, Russia

https://doi.org/10.1142/S0219025713500276Cited by:5 (Source: Crossref)

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: Δ_L = lim_ε→0 ∫_‖s-t‖<ε b_sb_tdsdt, where b_t is the annihilation process.

Keywords:

AMSC: 60H40

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