Properties of strong random operators generated by an Arratia flow

  • Ya. A. Korenovskaya

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
KorenovskayaY. A. “Properties of Strong Random Operators Generated by an Arratia Flow”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 2, Feb. 2017, pp. 157-72, http://umj.imath.kiev.ua/index.php/umj/article/view/1684.
Section
Research articles