Properties of the Flows Generated by Stochastic Equations with Reflection
- 34 Downloads
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
Unable to display preview. Download preview PDF.
- 1.I. I. Gikhman and A. V. Skorokhod, Stochastic Differential Equations and Their Applications [in Russian], Naukova Dumka, Kiev (1982).Google Scholar
- 4.N. Bouleau and F. Hirsch, Dirichlet Forms and Analysis on Wiener Space, de Gruyter, Berlin (1991).Google Scholar
- 7.P. Billingsley, Convergence of Probability Measures, Wiley, New York (1968).Google Scholar
- 8.O. Kallenberg, Foundations of Modern Probability, Springer, New York (2002).Google Scholar
- 9.H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge (1990).Google Scholar
- 10.N. Dunford and J. T. Schwartz, Linear Operators. Part 1: General Theory, Interscience, New York (1958).Google Scholar