{{Short description|Mathematical system for studying diffusion equations}} {{expert needed|Mathematics|reason=subject area outside original editor's area of expertise|date=December 2023}}
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 were a Riemannian metric.<ref name=":0">{{Cite web |last=Ambrosio |first=Luigi |authorlink=Luigi Ambrosio |title=Calculus and heat flow in metric measure spaces and spaces with Riemannian curvature bounds from below |url=https://www.maths.ox.ac.uk/system/files/attachments/L%20Ambrosio.pdf}}</ref><ref>{{Citation |last1=Ambrosio |first1=Luigi |title=Lecture 18: An Introduction to Otto's Calculus |date=2021 |url=https://doi.org/10.1007/978-3-030-72162-6_18 |work=Lectures on Optimal Transport |pages=211–228 |editor-last=Ambrosio |editor-first=Luigi |access-date=2023-12-20 |series=UNITEXT |place=Cham |publisher=Springer International Publishing |language=en |doi=10.1007/978-3-030-72162-6_18 |isbn=978-3-030-72162-6 |last2=Brué |first2=Elia |last3=Semola |first3=Daniele |s2cid=238959458 |editor2-last=Brué |editor2-first=Elia |editor3-last=Semola |editor3-first=Daniele|url-access=subscription }}</ref>
It is named after Felix Otto,<ref name=":0" /> who developed it in the late 1990s and published it in a 2001 paper on the geometry of dissipative evolution equations.<ref>{{Cite web |last1=Karatzas |first1=Ioannis |last2=Schachermayer |first2=Walter |last3=Tschiderer |first3=Bertram |date=21 November 2018 |title=Applying Itô calculus to Otto calculus |url=https://www.mat.univie.ac.at/~schachermayer/pubs/preprnts/prpr0173a.pdf}}</ref><ref name=":1">{{Cite journal |last=Otto |first=Felix |date=2001-01-31 |title=The geometry of dissipative evolution equations: the porous medium equation |url=http://www.tandfonline.com/doi/abs/10.1081/PDE-100002243 |journal=Communications in Partial Differential Equations |language=en |volume=26 |issue=1–2 |pages=101–174 |doi=10.1081/PDE-100002243 |s2cid=14799125 |issn=0360-5302|url-access=subscription }}</ref> Otto acknowledges inspiration from earlier work by David Kinderlehrer and conversations with Robert McCann and Cédric Villani.<ref name=":1" />
== See also == * Itô calculus
== References == {{Reflist}}
Category:Diffusion Category:Partial differential equations Category:Riemannian manifolds
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