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Time-changed Poisson processes

DSpace at IIT Bombay

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Field Value
 
Title Time-changed Poisson processes
 
Creator KUMAR, A
NANE, E
VELLAISAMY, P
 
Subject HIGHER-ORDER PDES
STABLE PROCESSES
RANDOM-WALKS
Hitting times
Inverse Gaussian process
Time-changed process, subordination
Tempered stable processes
Difference-differential equation
 
Description We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDEs) for these processes. In particular, we consider the time-changed Poisson processes where the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDEs. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDEs corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index 0 < beta < 1. when beta is a rational number. We then use this result to obtain the governing DDE for the mass function of the Poisson process time-changed by the tempered stable subordinator. Our results extend and complement the results in Baeumer et al. (2009) and Beghin and Orsingher (2009) in several directions. Published by Elsevier B.V.
 
Publisher ELSEVIER SCIENCE BV
 
Date 2012-06-26T08:32:38Z
2012-06-26T08:32:38Z
2011
 
Type Article
 
Identifier STATISTICS & PROBABILITY LETTERS,81(12)1899-1910
0167-7152
http://dx.doi.org/10.1016/j.spl.2011.08.002
http://dspace.library.iitb.ac.in/jspui/handle/100/14190
 
Language English