Time-changed Poisson processes
DSpace at IIT Bombay
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Title |
Time-changed Poisson processes
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Creator |
KUMAR, A
NANE, E VELLAISAMY, P |
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Subject |
HIGHER-ORDER PDES
STABLE PROCESSES RANDOM-WALKS Hitting times Inverse Gaussian process Time-changed process, subordination Tempered stable processes Difference-differential equation |
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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.
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Publisher |
ELSEVIER SCIENCE BV
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Date |
2012-06-26T08:32:38Z
2012-06-26T08:32:38Z 2011 |
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Type |
Article
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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 |
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Language |
English
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