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On the relative entropy of discrete-time Markov processes with given end-point densities

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1 Author(s)
A. Beghi ; Dipartimento di Elettronica e Inf., Padova Univ., Italy

Given a Markov process x(k) defined over a finite interval I=[0,N], I⊂Z we construct a process x*(k) with the same initial density as x, but a different end-point density, which minimizes the relative entropy of x and x*. It is shown that x* is a Markov process in the same reciprocal class as x. In the Gaussian case, the minimum relative entropy problem is related to a minimum energy LQG optimal control problem

Published in:

IEEE Transactions on Information Theory  (Volume:42 ,  Issue: 5 )