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Quantum gaussian processes

Quantum gaussian processes In this paper, we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces, and investigate the relation between their stochastic properties. Particularly, we are interested in Brownian bridges and quantum Ornstein-Uhlenbeck processes. We are even able to construct each of them in two different ways: to construct quantum processes based on ordinary Brownian bridges (Ornstein-Uhlenbeck processes resp.) or to solve the quantum S.D.E. driven by quantum Brownian motions. But essentially they are the same. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Quantum gaussian processes

Acta Mathematicae Applicatae Sinica , Volume 10 (3) – Jul 13, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1994 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02006861
Publisher site
See Article on Publisher Site

Abstract

In this paper, we will define the quantum Gaussian processes based on ordinary Gaussian processes by means of reproducing kernel Hilbert spaces, and investigate the relation between their stochastic properties. Particularly, we are interested in Brownian bridges and quantum Ornstein-Uhlenbeck processes. We are even able to construct each of them in two different ways: to construct quantum processes based on ordinary Brownian bridges (Ornstein-Uhlenbeck processes resp.) or to solve the quantum S.D.E. driven by quantum Brownian motions. But essentially they are the same.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References