Abstract
In this paper, we describe some properties of the Wasserstein-2 metric on the space of probability distributions of particular relevance to problems in control and signal processing. The resulting geodesics lead to interesting connections with Boltzmann entropy, heat equations (both linear and nonlinear), and suggest possible Riemannian structures on density functions. In particular, we observe similarities and connections with metrics originating in information geometry and prediction theory.
Mathematics Subject Classification. 34H05, 49J20.
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This paper is dedicated to our dear friend and colleague, Professor Bill Helton on the occasion of his 65th birthday.
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Tannenbaum, E., Georgiou, T., Tannenbaum, A. (2012). Optimal Mass Transport for Problems in Control, Statistical Estimation, and Image Analysis. In: Dym, H., de Oliveira, M., Putinar, M. (eds) Mathematical Methods in Systems, Optimization, and Control. Operator Theory: Advances and Applications, vol 222. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0411-0_22
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DOI: https://doi.org/10.1007/978-3-0348-0411-0_22
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