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EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES

Centro Vito Volterra, Università di Roma "Tor Vergata", 00133 Via Columbia 2, Roma, Italy

Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763, Korea

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KIMIAKI SAITÔ

Department of Mathematics, Meijo University, Nagoya 468, Japan

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https://doi.org/10.1142/S0219025709003513Cited by:12 (Source: Crossref)

Abstract

In this paper, we give a decomposition of the space of tempered distributions by the Cesàro norm, and for any we construct directly from the exotic trace an infinite dimensional separable Hilbert space H_c,2a-1 on which the exotic trace plays the role as the usual trace. This implies that the Exotic Laplacian coincides with the Volterra–Gross Laplacian in the Boson Fock space Γ(H_c,2a-1) over the Hilbert space H_c,2a-1. Finally we construct the Brownian motion naturally associated to the Exotic Laplacian of order 2a-1 and we find an explicit expression for the associated heat semigroup.

An errata has been published.

Keywords:

AMSC: 60H40

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