1,337 research outputs found
The Separation Principle in Stochastic Control, Redux
Over the last 50 years a steady stream of accounts have been written on the
separation principle of stochastic control. Even in the context of the
linear-quadratic regulator in continuous time with Gaussian white noise, subtle
difficulties arise, unexpected by many, that are often overlooked. In this
paper we propose a new framework for establishing the separation principle.
This approach takes the viewpoint that stochastic systems are well-defined maps
between sample paths rather than stochastic processes per se and allows us to
extend the separation principle to systems driven by martingales with possible
jumps. While the approach is more in line with "real-life" engineering thinking
where signals travel around the feedback loop, it is unconventional from a
probabilistic point of view in that control laws for which the feedback
equations are satisfied almost surely, and not deterministically for every
sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction
On time-reversibility of linear stochastic models
Reversal of the time direction in stochastic systems driven by white noise
has been central throughout the development of stochastic realization theory,
filtering and smoothing. Similar ideas were developed in connection with
certain problems in the theory of moments, where a duality induced by time
reversal was introduced to parametrize solutions. In this latter work it was
shown that stochastic systems driven by arbitrary second-order stationary
processes can be similarly time-reversed. By combining these two sets of ideas
we present herein a generalization of time-reversal in stochastic realization
theory.Comment: 10 pages, 4 figure
Likelihood Analysis of Power Spectra and Generalized Moment Problems
We develop an approach to spectral estimation that has been advocated by
Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance
extension problem, by Enqvist and Karlsson. The aim is to determine the power
spectrum that is consistent with given moments and minimizes the relative
entropy between the probability law of the underlying Gaussian stochastic
process to that of a prior. The approach is analogous to the framework of
earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a
generalization of the classical work by Burg and Jaynes on the maximum entropy
method. In the present paper we present a new fast algorithm in the general
case (i.e., for general Gaussian priors) and show that for priors with a
specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure
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