TY - JOUR AU - Ya. A. Korenovskaya PY - 2017/02/25 Y2 - 2024/03/28 TI - Properties of strong random operators generated by an Arratia flow JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 69 IS - 2 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/1684 AB - 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 $T_t$ preservestheir convergence. ER -