Volatility estimators and the inverse range process in a random volatility random walk and Wiener processes

The purpose of this paper is to study the mean, the variance, the probability distribution and the hazard rate of the inverse range process of an a-priori unknown volatility random walk. Motivation for this process arises when it is necessary to obtain statistics that pertain to a process volatility in addition to the usual variance statistics. As a result, range process statistics are indicated as an additional source of information in the study of processes’ volatility. Examples and applications are considered.