13,356 research outputs found
Linear filtering with fractional Brownian motion in the signal and observation processes
Integral equations for the mean-square estimate are obtained for the linear filtering problem, in which the noise generating the signal is a fractional Brownian motion with Hurst index h∈(3/4,1) and the noise in the observation process includes a fractional Brownian motion as well as a Wiener process. AMS subject classifications: 93E11, 60G20, 60G35
On the exchange of intersection and supremum of sigma-fields in filtering theory
We construct a stationary Markov process with trivial tail sigma-field and a
nondegenerate observation process such that the corresponding nonlinear
filtering process is not uniquely ergodic. This settles in the negative a
conjecture of the author in the ergodic theory of nonlinear filters arising
from an erroneous proof in the classic paper of H. Kunita (1971), wherein an
exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page
Thermodynamics of an interacting trapped Bose-Einstein gas in the classical field approximation
We present a convenient technique describing the condensate in dynamical
equilibrium with the thermal cloud, at temperatures close to the critical one.
We show that the whole isolated system may be viewed as a single classical
field undergoing nonlinear dynamics leading to a steady state. In our procedure
it is the observation process and the finite detection time that allow for
splitting the system into the condensate and the thermal cloud.Comment: 4 pages, 4 eps figures, final versio
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