Geodesic
A Duality Principle for the Legendre Transform
Journal of convex analysis, Tome 19 (2012) no. 3, pp. 609-63.

Voir la notice de l'article provenant de la source Heldermann Verlag

We present a duality principle for the Legendre transform that yields the shortest path between the graphs of functions and embodies the underlying Nash equilibrium. A useful feature of the algorithm for the shortest path obtained in this way is that its implementation has a local character in the sense that it is applicable at any point in the domain with no reference to calculations made earlier or elsewhere. The derived results are applied to optimal stopping games of Brownian motion and diffusion processes where the duality principle corresponds to the semiharmonic characterisation of the value function.
Classification : 49J35, 51M25, 60G40, 53C22, 60J65, 91A15
Mots-clés : Legendre transform, von Neumann's minimax theorem, Fenchel's duality theorem, shortest path between graphs, obstacles, geodesic, optimal stopping problem, game, free boundary problem, Brownian motion, diffusion, Markov process, superharmonic subharm 
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     author = {G. Peskir},
     title = {A {Duality} {Principle} for the {Legendre} {Transform}},
     journal = {Journal of convex analysis},
     pages = {609--63},
     publisher = {mathdoc},
     volume = {19},
     number = {3},
     year = {2012},
     url = {http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a1/}
}
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G. Peskir. A Duality Principle for the Legendre Transform. Journal of convex analysis, Tome 19 (2012) no. 3, pp. 609-63. http://geodesic.mathdoc.fr/item/JCA_2012_19_3_JCA_2012_19_3_a1/