Otto calculus
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Short description: Formal system
The Otto calculus (also known as Otto's calculus) is a mathematical system for studying diffusion equations that views the space of probability measures as an infinite dimensional Riemannian manifold by interpreting the Wasserstein distance as if it was a Riemannian metric.[1][2]
It is named after Felix Otto,[1] who developed it in the late 1990s and published it in a 2001 paper on the geometry of dissipative evolution equations.[3][4] Otto acknowledges inspiration from earlier work by David Kinderlehrer and conversations with Robert McCann and Cédric Villani.[4]
References
- ↑ 1.0 1.1 Ambrosio, L.. "Calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounds from below". https://www.maths.ox.ac.uk/system/files/attachments/L%20Ambrosio.pdf.
- ↑ Ambrosio, Luigi; Brué, Elia; Semola, Daniele (2021), Ambrosio, Luigi; Brué, Elia; Semola, Daniele, eds., "Lecture 18: An Introduction to Otto's Calculus" (in en), Lectures on Optimal Transport, UNITEXT (Cham: Springer International Publishing): pp. 211–228, doi:10.1007/978-3-030-72162-6_18, ISBN 978-3-030-72162-6, https://doi.org/10.1007/978-3-030-72162-6_18, retrieved 2023-12-20
- ↑ Karatzas, Ioannis; Schachermayer, Walter; Tschiderer, Bertram (21 November 2018). "Applying Itô calculus to Otto calculus". https://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0173a.pdf.
- ↑ 4.0 4.1 Otto, Felix (2001-01-31). "The geometry of dissipative evolution equations: the porous medium equation" (in en). Communications in Partial Differential Equations 26 (1–2): 101–174. doi:10.1081/PDE-100002243. ISSN 0360-5302. http://www.tandfonline.com/doi/abs/10.1081/PDE-100002243.
See also
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