On Stochastic Representation of Blow-Ups for Distributed Parameter Systems
This paper studies the regularity properties of stochastic representation of the stationary solution of the Fokker-Planck equation and related Dirichlet problem. When the correlation structure is exponential, we relate the representation process to the Ornstein-Uhlenbeck process. We derive some properties of blow-up identification by the singular points of the correlation structure.
KeywordsBlow-up Fokker-Planck equation Gaussian random field Hilbert space Ornstein-Uhlenbeck process Stochastic representation
Research was supported by the Slovak Research and Development Agency under the contract No. SK-AT-2015-0019. Corresponding author was supported by Fondecyt Proyecto Regular N 1151441 and WTZ Project SK 09/2016. Jozef Kiseľák was partially supported by grant VEGA MŠ SR 1/0344/14.
- 3.Evans, L.C.: Partial Differential Equations: Graduate Studies in Mathematics. American Mathematical Society, Providence (1998). 2nd edn. (2010)Google Scholar
- 6.Rybicki, G.B.: Notes on the Ornstein-Uhlenbeck Process, unpublished notes (1994)Google Scholar
- 8.Stehlík, M. On Stochastic Representation for Dirichlet Problem Solution. MendelNet (2006). Alfaknihy, Prague (in press)Google Scholar