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Chapitre D'ouvrage Année : 2012

Stochastic Analysis for the Complex Monge-Ampère Equation. (An Introduction to Krylov's Approach.)

Résumé

We here gather in a single note several original probabilistic works devoted to the analysis of the C^(1,1) regularity of the solution to the possibly degenerate complex Monge-Ampère equation. The whole analysis relies on a probabilistic writing of the solution as the value function of a stochastic optimal control problem. Such a representation has been introduced by Gaveau in the late 70's and used in an exhaustive way by Krylov in a series of papers published in the late 80's. All the arguments we here use follow from these seminal works.
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Dates et versions

hal-00555590 , version 1 (13-01-2011)
hal-00555590 , version 2 (11-06-2011)

Identifiants

Citer

François Delarue. Stochastic Analysis for the Complex Monge-Ampère Equation. (An Introduction to Krylov's Approach.). Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics. Lectures Notes in Mathematics 2038. (Editor: V. Guedj), Springer, pp.55-198, 2012, Lecture Notes in Mathematics, ⟨10.1007/978-3-642-23669-3⟩. ⟨hal-00555590v2⟩
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