Existence and joint continuity of local time of multi-parameter fractional Lévy processes

Abstract

In this paper, we introduce the definition of a multi-parameter fractional Lévy process and its local time, and show its decomposition. Using the decomposition, we prove existence and joint continuity of its local time.

Least squares estimator for Ornstein–Uhlenbeck processes driven by fractional Lévy processes from discrete observations

“…In this section, we briefly recall the definition and properties of FLP. More studies on the FLP can be found in Benassi et al (2002), Bender et al (2012), Engelke (2013), Fink et al (2011), Lacaux (2004, Lin et al (2009), Tikanmäki et al (2011) and the references therein.…”

Parameter estimation for Ornstein–Uhlenbeck processes driven by fractional Lévy process

“…For the study of fLp see Bender et al. [3], Fink and Klüppelberg [7], Lin and Cheng [18], Benassi et al. [1], Lacaux [16], Engelke [6] and the references therein.…”