The theory of Schroedinger bridges for diffusion processes is extended to discrete-time Markov chains, and to some problems for quantum discrete-time processes. Taking into account the past-future lack of symmetry of the discrete-time setting, results bear a striking resemblance to the classical ones. In particular, the solution of the path space maximum entropy problems is always obtained from the prior model by means of a suitable multiplicative functional transformation.
Schroedinger Bridges for Discrete-Time, Classical and Quantum Markovian Evolutions.
PAVON, MICHELE;TICOZZI, FRANCESCO
2010
Abstract
The theory of Schroedinger bridges for diffusion processes is extended to discrete-time Markov chains, and to some problems for quantum discrete-time processes. Taking into account the past-future lack of symmetry of the discrete-time setting, results bear a striking resemblance to the classical ones. In particular, the solution of the path space maximum entropy problems is always obtained from the prior model by means of a suitable multiplicative functional transformation.
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