A Note on α-stable and α-inverse Gaussian Laws

Satheesh, S.

doi:10.9734/ajpas/2022/v19i230465

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Proposition 31 the Function M1

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2022

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“…Remark 3.1. Now, in terms of Lévy processes, proposition 3.1 means that the GαLLP are obtained by randomising the time parameter of α-stable Lévy process in [18] by the unit exponential law. Similarly, by randomising the time parameter of symmetric α-stable Lévy process by the unit exponential, αLLP are obtained.…”

Section: Proposition 31 the Function Mmentioning

confidence: 99%

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A Generalized \(\alpha\)-Laplace Lévy Process

Satheesh

2022

AJPAS

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Random time changed Lévy Processes are getting increased attention of late as they can account for a variety of features in data. In this article we discuss \(\alpha\)-Laplace Lévy Process and a generalization of it. Both are random time changed \(\alpha\)-stable Lévy Processes. We obtained a characterization of \(\alpha\)-Laplace Lévy Process and discuss the first passage time distribution of a generalized \(\alpha\)-Laplace Lévy Process. Interestingly, this first passage time follows a discrete distribution.

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Section: Proposition 31 the Function Mmentioning

confidence: 99%

“…Here we refer to them as α-stable laws. [18] used this to define and discuss α-stable Lévy processes. Theorem 1.6.…”

Section: Introductionmentioning

confidence: 99%