Otto calculus
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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]
See also
[edit]References
[edit]- ^ a b Ambrosio, L. "Calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounds from below" (PDF).
- ^ Ambrosio, Luigi; Brué, Elia; Semola, Daniele (2021), Ambrosio, Luigi; Brué, Elia; Semola, Daniele (eds.), "Lecture 18: An Introduction to Otto's Calculus", 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, S2CID 238959458, retrieved 2023-12-20
- ^ Karatzas, Ioannis; Schachermayer, Walter; Tschiderer, Bertram (21 November 2018). "Applying Itô calculus to Otto calculus" (PDF).
- ^ a b Otto, Felix (2001-01-31). "The geometry of dissipative evolution equations: the porous medium equation". Communications in Partial Differential Equations. 26 (1–2): 101–174. doi:10.1081/PDE-100002243. ISSN 0360-5302. S2CID 14799125.
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