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- Title
EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES.
- Authors
ACCARDI, LUIGI; UN CIG JI; SAITÔ, KIMIAKI
- Abstract
In this paper, we give a decomposition of the space of tempered distributions by the Cesàro norm, and for any $a > \frac{1}{2}$ we construct directly from the exotic trace an infinite dimensional separable Hilbert space Hc,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(Hc,2a-1) over the Hilbert space Hc,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.
- Subjects
LAPLACIAN operator; STOCHASTIC processes; DECOMPOSITION method; HILBERT space; WIENER processes; DISTRIBUTION (Probability theory)
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2009, Vol 12, Issue 1, p1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025709003513