Kolmogorov equations and weak order analysis for SPDEs with nonlinear diffusion coefficient
By Charles-Edouard Br'ehier, Arnaud Debussche. Journal des Mathématiques Pures et Appliquées, 2017
51 citations recorded by the source corpus.
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.
Subfields: Astronomy and Astrophysics, Computational Mechanics, Finance
View Paper: https://www.semanticscholar.org/paper/2caf867967529e13950f34385d99c247af148de9
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Citations in the corpus
- Orders of convergence in the averaging principle for SPDEs: The case of a stochastically forced slow component (2018, methodology): “We refer to [7] for a recent overview of this topic and for further results.”