Transfer of absolute continuity by a flow generated by a stochastic equation with reflection

• Date: 2006
• Main Authors: Pilipenko, A. Yu., Пилипенко, А. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3562
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let $\varphi_t(x),\quad x \in \mathbb{R}_+ $, be a value taken at time $t \geq 0$ by a solution of stochastic equation with normal reflection from the hyperplane starting at initial time from $x$. We characterize an absolutely continuous (with respect to the Lebesgue measure) component and a singula...