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Journal article
On Fractional Levy Processes: Tempering, Sample Path Properties and Stochastic Integration
Journal of statistical physics, v 178(4), pp 954-985
01 Feb 2020
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Abstract
We define two new classes of stochastic processes, called tempered fractional Levy process of the first and second kinds (TFLP and TFLP II, respectively). TFLP and TFLP II make up very broad finite-variance, generally non-Gaussian families of transient anomalous diffusion models that are constructed by exponentially tempering the power law kernel in the moving average representation of a fractional Levy process. Accordingly, the increment processes of TFLP and TFLP II display semi-long range dependence. We establish the sample path properties of TFLP and TFLP II. We further use a flexible framework of tempered fractional derivatives and integrals to develop the theory of stochastic integration with respect to TFLP and TFLP II, which may not be semimartingales depending on the value of the memory parameter and choice of marginal distribution.
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Details
- Title
- On Fractional Levy Processes: Tempering, Sample Path Properties and Stochastic Integration
- Creators
- B. Cooper Boniece - Washington University in St. LouisGustavo Didier - Tulane UniversityFarzad Sabzikar - Iowa State University
- Publication Details
- Journal of statistical physics, v 178(4), pp 954-985
- Publisher
- Springer Nature
- Number of pages
- 32
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000513280000006
- Scopus ID
- 2-s2.0-85077718517
- Other Identifier
- 991021862259404721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Physics, Mathematical