Ukrainian Mathematical Journal

, Volume 57, Issue 8, pp 1262–1274 | Cite as

Properties of the Flows Generated by Stochastic Equations with Reflection

  • A. Yu. Pilipenko


We consider the properties of a random set ϕ t (ℝ + d ), where ϕ t (x) is a solution of a stochastic differential equation in ℝ + d with normal reflection from the boundary that starts from a point x. We characterize inner and boundary points of the set ϕ t (ℝ + d ) and prove that the Hausdorff dimension of the boundary ∂ϕ t (ℝ + d ) does not exceed d − 1.


Differential Equation Boundary Point Stochastic Differential Equation Hausdorff Dimension Stochastic Equation 
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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • A. Yu. Pilipenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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