TY - JOUR
AU - Ya. A. Korenovskaya
PY - 2017/02/25
Y2 - 2022/09/26
TI - Properties of strong random operators generated by an Arratia flow
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 2
SE - Research articles
DO -
UR - http://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 -