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On Stochastic Representation of Blow-Ups for Distributed Parameter Systems

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 10187)

Abstract

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.

Keywords

  • Blow-up
  • Fokker-Planck equation
  • Gaussian random field
  • Hilbert space
  • Ornstein-Uhlenbeck process
  • Stochastic representation

M. Stehlík—I thank to Professor Lyuben Valkov for his invitation.

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Acknowledgments

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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Stehlík, M., Kiseľák, J. (2017). On Stochastic Representation of Blow-Ups for Distributed Parameter Systems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_12

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_12

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