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.
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This research is supported in part by the National Natural Science Foundation of China and National Science Foundation of USA under Grant DDM-8721709.
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Wang, Y. Quantum gaussian processes. Acta Mathematicae Applicatae Sinica 10, 315–327 (1994). https://doi.org/10.1007/BF02006861
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DOI: https://doi.org/10.1007/BF02006861