Continuity and variation analysis of fractional uncertain processes

The canonical Liu process is a stationary and independent increment uncertain process with normal increments. As one of the most important types of uncertain processes, the fractional Liu process is presented as a variant of canonical Liu process, which has a potential application in modeling an irregular movement with long memory in a system associated with human uncertainty rather than stochastic factors. This paper is devoted to studying the mathematical properties of fractional Liu process such as the increments, variation and sample continuity, especially the Hölder continuity of its sample paths. The obtained results lay the theoretical foundation and promote the applications of fractional Liu processes.