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 Levy-Laplacian is obtained as the usual Volterra-Gross Laplacian using the Cesaro Hilbert space as initial space of our process as well as multiplicity space of the associated white noise.
Accardi, L., Barhoumi, A., Ouerdiane, H. (2006). A quantum approach to Laplace operators. INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS, 9(2), 215-248 [10.1142/S0219025706002329].
A quantum approach to Laplace operators
ACCARDI, LUIGI;
2006-06-01
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 Levy-Laplacian is obtained as the usual Volterra-Gross Laplacian using the Cesaro Hilbert space as initial space of our process as well as multiplicity space of the associated white noise.| File | Dimensione | Formato | |
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