Journal ArticleDOI
Fractional Poisson Process Time-Changed by Lévy Subordinator and Its Inverse
TLDR
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
Citations
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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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BookDOI
Financial modelling with jump processes
Rama Cont,Peter Tankov +1 more
TL;DR: In this article, the authors provide a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists.
Book
Lévy Processes and Stochastic Calculus
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
Book
The statistical analysis of series of events
David Cox,Peter A W Lewis +1 more
TL;DR: This monograph is intended as a survey of some of the problems in theoretical statistics that stem from this sort of data, and has tried to give a simple description, with numerical examples, of the main methods that have been proposed.
A singular integral equation with a generalized mittag leffler function in the kernel
TL;DR: In this article, a linear operator of order functions of order (1.2) is defined and an operator of fractional integration is employed to prove results on the solutions of the integral equation.