Discrete-time Gauss-Markov processes with fixed reciprocal dynamics

Motivated by a problem considered earlier by Schrodinger [1][2], Jamison [3][4] and others, we examine in this paper the construction of Gauss-Markov processes with xed reciprocal dynamics. Given the class of reciprocal processes specied by a second-order model, a procedure is described for constructing a Markov process in the class with preassigned marginal probability densities at the end points. The problem of changing the nal density of a Gauss-Markov process while remaining in the same reciprocal class is also examined, and is interpreted in terms of an estimation problem.