3,259 research outputs found
Stochastic Wiener Filter in the White Noise Space
In this paper we introduce a new approach to the study of filtering theory by
allowing the system's parameters to have a random character. We use Hida's
white noise space theory to give an alternative characterization and a proper
generalization to the Wiener filter over a suitable space of stochastic
distributions introduced by Kondratiev. The main idea throughout this paper is
to use the nuclearity of this spaces in order to view the random variables as
bounded multiplication operators (with respect to the Wick product) between
Hilbert spaces of stochastic distributions. This allows us to use operator
theory tools and properties of Wiener algebras over Banach spaces to proceed
and characterize the Wiener filter equations under the underlying randomness
assumptions
A transverse Hamiltonian variational technique for open quantum stochastic systems and its application to coherent quantum control
This paper is concerned with variational methods for nonlinear open quantum
systems with Markovian dynamics governed by Hudson-Parthasarathy quantum
stochastic differential equations. The latter are driven by quantum Wiener
processes of the external boson fields and are specified by the system
Hamiltonian and system-field coupling operators. We consider the system
response to perturbations of these energy operators and introduce a transverse
Hamiltonian which encodes the propagation of the perturbations through the
unitary system-field evolution. This provides a tool for the infinitesimal
perturbation analysis and development of optimality conditions for coherent
quantum control problems. We apply the transverse Hamiltonian variational
technique to a mean square optimal coherent quantum filtering problem for a
measurement-free cascade connection of quantum systems.Comment: 12 pages, 1 figure. A brief version of this paper will appear in the
proceedings of the IEEE Multi-Conference on Systems and Control, 21-23
September 2015, Sydney, Australi
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