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Preprint
On fractional Lévy processes: tempering, sample path properties and stochastic integration
arXiv.org
01 Oct 2019
Abstract
We define two new classes of stochastic processes, called tempered fractional L\'{e}vy process of the first and second kinds (TFLP and TFLP \(I\!I\), respectively). TFLP and TFLP \(I\!I\) 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 L\'{e}vy process. Accordingly, the increment processes of TFLP and TFLP \(I\!I\) display semi-long range dependence. We establish the sample path properties of TFLP and TFLP \(I\!I\). 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 \(I\!I\), 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 Lévy processes: tempering, sample path properties and stochastic integration
- Creators
- Benjamin Cooper BonieceGustavo DidierFarzad Sabzikar
- Publication Details
- arXiv.org
- Publisher
- Cornell University Library, arXiv.org; Ithaca
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861870704721