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Title: Time-changed Poisson processes of order $k$ Authors:  Neelesh Shankar Upadhye - Indian Institute of Technology Madras (India) [presenting]
Ayushi Sengar - IIT Madras (India)
Aditya Maheshwari - IIM Indore (India)
Abstract: The aim is to study the Poisson process of order $k$ (PPoK) time-changed with an independent L\'evy subordinator and its inverse, which we call respectively, as TCPPoK-I and TCPPoK-II, through various distributional properties, long-range dependence and limit theorems for the PPoK and the TCPPoK-I. Further, we study the governing difference-differential equations of the TCPPoK-I for the case inverse Gaussian subordinator. Similarly, we investigate the distributional properties, asymptotic moments and the governing difference-differential equation of TCPPoK-II. As an application to ruin theory, we give a governing differential equation of ruin probability in insurance ruin using these processes. Finally, we present some simulated sample paths of both the processes.