publication . Article . Other literature type . Preprint . 2011

tempered stable laws as random walk limits

Chakrabarty, Arijit; Meerschaert, Mark M.;
Open Access
  • Published: 01 Aug 2011 Journal: Statistics & Probability Letters, volume 81, pages 989-997 (issn: 0167-7152, Copyright policy)
  • Publisher: Elsevier BV
Abstract
Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk models that converge to a tempered stable law under a triangular array scheme. Since tempered stable laws and processes are useful in statistical physics, these random walk models can provide a basic physical model for the underlying physical phenomena.
Subjects
free text keywords: Statistics, Probability and Uncertainty, Statistics and Probability, Stable process, Infinity, media_common.quotation_subject, media_common, Power law, Probability theory, Triangular array, Infinite divisibility, Random walk, Mathematics, Probability measure, Law, Statistics, Mathematics - Probability
Funded by
NSF| Stochastic Models for Anomalous Diffusion
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0803360
  • Funding stream: Directorate for Mathematical & Physical Sciences | Division of Mathematical Sciences
,
NSF| Collaborative Research: The Children's Research Initiative (CRI): Integrative Approaches: Perception-Action Foundations of Early Tool Use
Project
  • Funder: National Science Foundation (NSF)
  • Project Code: 0125486
  • Funding stream: Directorate for Social, Behavioral & Economic Sciences | Division of Behavioral and Cognitive Sciences
,
NIH| Fast numerical modeling of medical ultrasound for therapy and imaging
Project
  • Funder: National Institutes of Health (NIH)
  • Project Code: 5R01EB012079-03
  • Funding stream: NATIONAL INSTITUTE OF BIOMEDICAL IMAGING AND BIOENGINEERING
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NSF| Collaborative Research: Geomorphic transport laws, landscape evolution, and fractional calculus
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  • Funder: National Science Foundation (NSF)
  • Project Code: 0823965
  • Funding stream: Directorate for Geosciences | Division of Earth Sciences
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publication . Article . Other literature type . Preprint . 2011

tempered stable laws as random walk limits

Chakrabarty, Arijit; Meerschaert, Mark M.;