# Properties of strong random operators generated by an Arratia flow

### Abstract

We study the properties of strong random operators $T_t$ in $L_2(R)$ used to describe the shifts of the functions along an Arratia flow. We prove the formula of change of variables for the Arratia flow. As a consequence of this formula, we establish sufficient conditions for compact sets $K \subset L_2(R)$ under which $T_t$ has a continuous modification on $K$. We also present necessary and sufficient conditions for the convergent sequences in $L_2(R)$ under which the operator $T_t$ preserves their convergence.
Published

25.02.2017

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 69, no. 2, Feb. 2017, pp. 157-72, http://umj.imath.kiev.ua/index.php/umj/article/view/1684.

Issue

Section

Research articles