2017
Том 69
№ 9

# Properties of strong random operators generated by an Arratia flow

Korenovskaya Ya. A.

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.

Citation Example: Korenovskaya Ya. A. Properties of strong random operators generated by an Arratia flow // Ukr. Mat. Zh. - 2017. - 69, № 2. - pp. 157-172.