Scaling limits of a heavy tailed Markov renewal process
نویسنده
چکیده
In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α-stable regenerative set. We then apply these results to the strip wetting model which is a random walk S constrained above a wall and rewarded or penalized when it hits the strip [0,∞) × [0, a] where a is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.
منابع مشابه
On Scaling Limits of Arrival Processes with Long-Range Dependence
Various classes of arrival processes in telecommunication traffic modeling based on heavy-tailed interarrival time distributions exhibit long-range dependence. This includes arrival rate processes of Anick-MitraSondhi (AMS) type where the rate process is an on/off-process with heavy-tailed on-period distribution and/or off-period distribution, as well as generalized Kosten type models (infinite...
متن کاملExtended Geometric Processes: Semiparametric Estimation and Application to ReliabilityImperfect repair, Markov renewal equation, replacement policy
Lam (2007) introduces a generalization of renewal processes named Geometric processes, where inter-arrival times are independent and identically distributed up to a multiplicative scale parameter, in a geometric fashion. We here envision a more general scaling, not necessar- ily geometric. The corresponding counting process is named Extended Geometric Process (EGP). Semiparametric estimates are...
متن کاملar X iv : 0 80 9 . 16 12 v 1 [ m at h . PR ] 9 S ep 2 00 8 CORRELATED CONTINUOUS TIME RANDOM WALKS
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. This paper develops scaling limits and governing equations in the case of correl...
متن کاملCorrelated continuous time random walks
Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy-tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy-tailed jumps, and the time-fractional version codes heavy-tailedwaiting times. This paper develops scaling limits and governing equations in the case of correla...
متن کاملANALYSIS OF FINITE BUFFER RENEWAL INPUT QUEUE WITH BALKING AND MARKOVIAN SERVICE PROCESS
This paper presents the analysis of a renewal input finite buffer queue wherein the customers can decide either to join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed by an underlying $m$-state Markov chain. Employing the supplementary variable and imbedded Markov chain techniques, the steady-state system length distributions at pre...
متن کامل