Properties of the Flows Generated by Stochastic Equations with Reflection
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.
KeywordsDifferential Equation Boundary Point Stochastic Differential Equation Hausdorff Dimension Stochastic Equation
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