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arXiv · 2105.00988

Tempered positive Linnik processes and their representations

Lorenzo Torricelli·Lucio Barabesi·Andrea Cerioli
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Abstract

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations gives rise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling.

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Lorenzo Torricelli, Lucio Barabesi, Andrea Cerioli. 2022-06-06. Tempered positive Linnik processes and their representations. https://arxiv.org/abs/2105.00988

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