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

Agnieszka Wyłomańska

Physica A: Statistical Mechanics and its Applications, 2012, vol. 391, issue 22, 5685-5696

Abstract: In the last decade the subordinated processes have become popular and have 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.

Keywords: Subordination; Brownian motion; Tempered stable; Diffusion; Anomalous diffusion; Calibration (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:391:y:2012:i:22:p:5685-5696

DOI: 10.1016/j.physa.2012.05.072

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