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Föllmer, Hans; Gantert, Nina

Entropy minimization and Schrödinger processes in infinite dimensions. (English) Zbl 0876.60063

Ann. Probab. 25, No. 2, 901-926 (1997).
A Schrödinger process is a Markov process that can be expressed as a mixture of Brownian bridges. In finite-dimensional spaces, they appear in a problem of large deviation involving minimization of the relative entropy with fixed marginals, which has been considered first by Schrödinger, and can also be obtained as a Doob’s \(h\)-transform of Brownian motion for a certain class of space-time harmonic functions. The paper investigates the analogous connections in infinite dimension.
Reviewer: J.Bertoin (Paris)

Cited in 1 Review
Cited in 10 Documents

MSC:

60J65 Brownian motion
60F10 Large deviations
60J45 Probabilistic potential theory
60J25 Continuous-time Markov processes on general state spaces
94A17 Measures of information, entropy

Keywords:

Schrödinger process; Brownian bridges; large deviation; space-time harmonic functions
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\textit{H. Föllmer} and \textit{N. Gantert}, Ann. Probab. 25, No. 2, 901--926 (1997; Zbl 0876.60063)
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