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
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Integro-differential equations linked to compound birth processes with infinitely divisible addends
TL;DR: In this paper, the authors considered a cumulative model where, instead of a renewal process (as in the Poisson case), a linear birth (or Yule) process is used.
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Fractional Skellam Process of Order $k$
K. K. Kataria,M. Khandakar +1 more
TL;DR: In this article, a fractional version of the Skellam process of order $k$ by time-changing it with an independent inverse stable subordinator is introduced and an integral representation for its one-dimensional distributions and their governing system of fractional differential equations are obtained.
Journal ArticleDOI
Convoluted fractional Poisson process of order <i>k</i>
TL;DR: In this article , the authors defined a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations, and obtained its one-dimensional distribution by using the Laplace transform of its state probabilities.
Journal ArticleDOI
Skellam and time-changed variants of the generalized fractional counting process
TL;DR: In this article , the generalized fractional Skellam process (GFSP) is considered by time-changing it with an independent inverse stable subordinator, and it is observed that the GFSP is a Skellham type version of the generalized fractional counting process (GFCP), which is a fractional variant of the GCP.
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Skellam and Time-Changed Variants of the Generalized Fractional Counting Process
TL;DR: In this paper, the generalized fractional Skellam process (GFSP) is considered by time-changing it with an independent inverse stable subordinator, and its distributional properties such as the probability mass function, probability generating function, mean, variance and covariance are obtained.
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.