A Generalized \(\alpha\)-Laplace Lévy Process
S. Satheesh *
School of Data Analytics, M. G. University, Kottayam - 686 560, India.
*Author to whom correspondence should be addressed.
Abstract
Random time changed Lévy Processes are getting increased attention of late as they can account for a variety of features in data. In this article we discuss \(\alpha\)-Laplace Lévy Process and a generalization of it. Both are random time changed \(\alpha\)-stable Lévy Processes. We obtained a characterization of \(\alpha\)-Laplace Lévy Process and discuss the first passage time distribution of a generalized \(\alpha\)-Laplace Lévy Process. Interestingly, this first passage time follows a discrete distribution.
Keywords: \(\alpha\)-Laplace, characterization, first passage time, Laplace transform, Lévy Processes, moment generating function