Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2017

Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient

Résumé

We provide new regularity results for the solutions of the Kolmogorov equation associated to a SPDE with nonlinear diffusion coefficients and a Burgers type nonlinearity. This generalizes previous results in the simpler cases of additive or affine noise. The basic tool is a discrete version of a two sided stochastic integral which allows a new formulation for the derivatives of these solutions. We show that this can be used to generalize the weak order analysis performed in [16]. The tools we develop are very general and can be used to study many other examples of applications.
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Dates et versions

hal-01481966 , version 1 (03-03-2017)
hal-01481966 , version 2 (07-06-2018)

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Charles-Edouard Bréhier, Arnaud Debussche. Kolmogorov Equations and Weak Order Analysis for SPDES with Nonlinear Diffusion Coefficient. 2017. ⟨hal-01481966v1⟩
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