ON THE RELATIVE ENTROPY OF DISCRETE-TIME MARKOV-PROCESSES WITH GIVEN END-POINT DENSITIES

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