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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Posted Content
Parameter estimation for fractional Poisson processes.
TL;DR: In this paper, a formal estimation procedure for parameters of the fractional Poisson process (fPp) is proposed to make the fPp model more flexible by permitting non-exponential, heavy-tailed distributions of interarrival times and different scaling properties.
Journal ArticleDOI
Correlation Structure of Time-Changed Lévy Processes
TL;DR: In this article, the correlation function for time-changed L evy processes has been studied in the context of continuous time random walks, where the second-order correlation function of a continuous-time random walk is defined.
Journal ArticleDOI
Inverse Tempered Stable Subordinators
TL;DR: In this paper, the first-exit time of a tempered β-stable subordinator, also called inverse tempered stable (ITS) subordinator was investigated and the limiting form of the ITS density and its k-th order derivatives were derived as the space variable x → 0 +.
Journal ArticleDOI
Applications of inverse tempered stable subordinators
TL;DR: This paper shows that the probability density function of an inverse tempered stable subordinator solves a tempered time-fractional diffusion equation, and its “folded” density solves a temperamental telegraph equation.
Proceedings ArticleDOI
Efficient simulation of gamma and variance-gamma processes
Avramidis,L'Ecuyer,Tremblay +2 more
TL;DR: In this paper, the authors study algorithms for sampling discrete-time paths of a gamma process and a variance-gamma process, defined as a Brownian process with random time change obeying a Gamma process, and compare the variance and efficiency of ordinary Monte Carlo and quasi-Monte Carlo for an example of financial option pricing with the variancegamma model.