2016/01/07 by Francisco Delgado‐Vences, Delgado-Vences, Francisco J., Franco Flandoli +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR) #Statistical Mechanics and Entropy #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1601.01503
openalex publication_date 2016/01/07 · openalex created_date 2022/09/28 · openalex updated_date 2026/08/01
We propose a numerical solution for the solution of the\nFokker-Planck-Kolmogorov (FPK) equations associated with stochastic partial\ndifferential equations in Hilbert spaces.\n The method is based on the spectral decomposition of the Ornstein-Uhlenbeck\nsemigroup associated to the Kolmogorov equation. This allows us to write the\nsolution of the Kolmogorov equation as a deterministic version of the\nWiener-Chaos Expansion. By using this expansion we reformulate the Kolmogorov\nequation as a infinite system of ordinary differential equations, and by\ntruncation it we set a linear finite system of differential equations. The\nsolution of such system allow us to build an approximation to the solution of\nthe Kolmogorov equations. We test the numerical method with the Kolmogorov\nequations associated with a stochastic diffusion equation, a Fisher-KPP\nstochastic equation and a stochastic Burgers Eq. in dimension 1.\n