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Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse
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In this paper, the authors studied the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinators, which they call TCFPP-I and TC FPP-II, respectively.Abstract:
In this paper, we study the fractional Poisson process (FPP) time-changed by an independent Levy subordinator and the inverse of the Levy subordinator, which we call TCFPP-I and TCFPP-II, respectively. Various distributional properties of these processes are established. We show that, under certain conditions, the TCFPP-I has the long-range dependence property, and also its law of iterated logarithm is proved. It is shown that the TCFPP-II is a renewal process and its waiting time distribution is identified. The bivariate distributions of the TCFPP-II are derived. Some specific examples for both the processes are discussed. Finally, we present simulations of the sample paths of these processes.read more
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Journal ArticleDOI
Time-changed Poisson processes of order k
TL;DR: In this article, the Poisson process of order k (PPoK) time-changed with an independent Levy subordinator and its inverse was studied, which they called TCPPoK-I and TCPPoK-II.
Journal ArticleDOI
Non-homogeneous space-time fractional Poisson processes
TL;DR: The space-time fractional Poisson process (STFPP) as mentioned in this paper is a generalization of the TFPP and the space fractional poisson process, defined by Orsingher and Poilto (2012).
Journal ArticleDOI
Linnik Lévy process and some extensions
TL;DR: In this paper, the Linnik Levy process (LLP) is proposed to model leptokurtic data with heavy-tailed behavior, and the authors give a step-by-step procedure of the parameters estimation and calibrate the parameters of the LLP with the Arconic Inc equity data taken from Yahoo finance.
Dissertation
Non-stationary processes and their application to financial high-frequency data
TL;DR: In this article, a fractional non-homogeneous Poisson process (FNPP) was introduced by applying a random time change to the standard poisson process and the authors derived its non-local governing equation.
Journal ArticleDOI
Subordinated compound Poisson processes of order k
TL;DR: In this article, the compound Poisson processes of order $k$ (CPPoK) were introduced and its properties were discussed, using mixture of tempered stable subordinator and its right continuous inverse, the two subordinated CPPoK with various distributional properties were studied.
References
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Journal ArticleDOI
Stable densities under change of scale and total variation inequalities
TL;DR: In this article, it was shown that if q is the density of a symmetric stable density, then the graph of q(x) intersects with q(cq(cx) at only two points.
Journal Article
A fractional generalization of the Poisson processes
TL;DR: In this article, a non-Markovian renewal process with a waiting time distribution described by the Mittag-Leffler function is analyzed, and it is shown that this distribution plays a fundamental role in the infinite thinning procedure of a generic renewal process governed by a power asymptotic waiting time.
Posted Content
A fractional generalization of the Poisson processes
TL;DR: In this article, a non-Markovian renewal process with a waiting time distribution described by the Mittag-Leffler function is analyzed, and it is shown that this distribution plays a fundamental role in the infinite thinning procedure of a generic renewal process governed by a power asymptotic waiting time.
Journal ArticleDOI
Fractional Poisson Law
O. N. Repin,A. I. Saichev +1 more
TL;DR: In this article, the authors considered a Poisson process with random intensity for which the distribution of intervals between jumps is described by an equation with fractional derivatives and obtained the generating function of the jump number in explicit form.