Generalized fractional Laplace motion

Abstract

In this paper, a new stochastic process called generalized fractional Laplace motion (GFLM) is introduced. This process is obtained by superposition of nnth-order fractional Brownian motion (nn-FBM) as outer process and gamma process as inner process. It is shown that nn-FBM process has long-range-dependence (LRD), persistence of signs LRD and persistence of magnitudes LRD properties. Distributional properties of GFLM such as probability density function, moments, covariance structure are established. The fractional partial differential equation governed by the GFLM density is obtained. Finally, it is shown that GFLM has LRD property for all H∈(n−1,n)H∈(n−1,n), similar to the nn-FBM case.