Arithmetic Brownian motion subordinated by tempered stable and inverse tempered stable processes |
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Authors: | Agnieszka Wy?omańska |
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Institution: | Hugo Steinhaus Center, Institute of Mathematics and Computer Science, Wroclaw University of Technology, Janiszewskiego 14a, 50-370 Wroc?aw, Poland |
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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. |
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Keywords: | Subordination Brownian motion Tempered stable Diffusion Anomalous diffusion Calibration |
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