Stochastic Analysis for the Complex Monge-Ampère Equation. (An Introduction to Krylov's Approach.) - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2010

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)

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  • HAL Id : hal-00555590 , version 1

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François Delarue. Stochastic Analysis for the Complex Monge-Ampère Equation. (An Introduction to Krylov's Approach.). 2010. ⟨hal-00555590v1⟩
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