2017
Том 69
№ 6

All Issues

Properties of the Flows Generated by Stochastic Equations with Reflection

Pilipenko A. Yu.

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Abstract

We consider properties of a random set $\varphi_t(\mathbb{R}_+^d)$, where $\varphi_t(x)$ is a solution of a stochastic differential equation in $\mathbb{R}_+^d$ with normal reflection on the boundary starting at the point $x$. We perform the characterization of inner and boundary points of the set $\varphi_t(\mathbb{R}_+^d)$. We prove that the Hausdorff dimension of the boundary $\partial \varphi_t(\mathbb{R}_+^d)$ is not greater than $d - 1$.

English version (Springer): Ukrainian Mathematical Journal 57 (2005), no. 8, pp 1262-1274.

Citation Example: Pilipenko A. Yu. Properties of the Flows Generated by Stochastic Equations with Reflection // Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1069 – 1078.

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