On Stochastic Representation of Blow-Ups for Distributed Parameter Systems

  • Milan StehlíkEmail author
  • Jozef Kiseľák
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10187)


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.


Blow-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.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Applied Statistics and Linz Institute of TechnologyJohannes Kepler University in LinzLinzAustria
  2. 2.Institute of StatisticsUniversidad de ValparaísoValparaísoChile
  3. 3.Institute of Mathematics, Faculty of ScienceP.J. Šafárik University in KošiceKošiceSlovakia

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