A QUANTUM APPROACH TO LAPLACE OPERATORS-Reference-Cited by-同舟云学术

A QUANTUM APPROACH TO LAPLACE OPERATORS

Published:2006-06 Issue:02 Volume:09 Page:215-248
ISSN:0219-0257
Container-title:Infinite Dimensional Analysis, Quantum Probability and Related Topics
language:en
Short-container-title:Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

Author:

ACCARDI LUIGI¹,BARHOUMI ABDESSATAR²,OUERDIANE HABIB³

Affiliation:

1. Centro Vito Volterra, Facultà di Economia, Università di Tor Vergata, Via di Tor Vergata, 00133 Roma, Italy

2. Nabeul Preparatory Engineering Institute, Mrezgua University Compus, 8000 Nabeul, Tunisia

3. Department of Mathematics, Faculty of Sciences of Tunis, University of Tunis El Manar, 1060 Tunis, Tunisia

Abstract

In this paper, a theory of stochastic processes generated by quantum extensions of Laplacians is developed. Representations of the associated heat semigroups are discussed by means of suitable time shifts. In particular the quantum Brownian motion associated to the Lévy–Laplacian is obtained as the usual Volterra–Gross Laplacian using the Cesàro Hilbert space as initial space of our process as well as multiplicity space of the associated white noise.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Mathematical Physics,Statistics and Probability,Statistical and Nonlinear Physics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219025706002329

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