Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes

Abstract

In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called arithmetic Brownian motion). The first one, so called normal tempered stable, is related to the tempered stable subordinator, while the second one - to the inverse tempered stable process. We compare the main properties (such as probability density functions, Laplace transforms, ensemble averaged mean squared displacements) of such two subordinated processes and propose the parameters' estimation procedures. Moreover we calibrate the analyzed systems to real data related to indoor air quality.

References in corpus (6)

• Diffusion and Relaxation Controlled by Tempered α-stable Processes
• Subordinated diffusion and CTRW asymptotics
• First passage time processes and subordinated SLE
• Two-time scale subordination in physical processes with long-term memory
• Anomalous diffusion models: different types of subordinator distribution
• Swarms with canonical active Brownian motion

Cited by in corpus (4)

• Fractional Brownian motion time-changed by gamma and inverse gamma process
• Tempered relaxation equation and related generalized stable processes
• Modified cumulative distribution function in application to waiting time analysis in CTRW scenario
• The subordinated processes controlled by a family of subordinators and corresponding Fokker-Planck type equations