On a Stochastic Parabolic Integral Equation

  • Wolfgang Desch
  • Stig-Olof Londen


In this article we analyze the stochastic parabolic integral equation
$$ u\left( {t,x,\omega } \right) = c_\alpha t^{ - 1 + \alpha } *\Delta u + \sum\limits_{k = 1}^\infty {\smallint _0^t g^k \left( {s,x,\omega } \right)} dw_s^k , $$
where t ≥ 0, x ∈ ℝ d , α ∈ (1/2, 1) and ω ∈ Ω. We take w k t ⌝ k = 1, 2, . . . to be a family of independent \( \mathcal{F}_t \) -adapted Wiener processes defined on a probability space \( \left( {\Omega ,\mathcal{F},P} \right) \) . Here \( \mathcal{F}_t \subset \mathcal{F}{\text{and }}\mathcal{F}_t \) is an increasing filtration.

By applying and modifying the method of Krylov we obtain existence and regularity results in L p -spaces, p ≥ 2.


Lumer Volume Maximal Regularity Lebesgue Point Stochastic Heat Equation Stochastic Convolution 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • Wolfgang Desch
    • 1
  • Stig-Olof Londen
    • 2
  1. 1.Institut für MathematikUniversität GrazGrazAustria
  2. 2.Institute of MathematicsHelsinki University of TechnologyEspooFinland

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