The covariance of the backward and forward recurrence times in a renewal process: the stationary case and asymptotics for the ordinary case

2019 ◽  
Vol 35 (1) ◽  
pp. 51-62 ◽  
Author(s):  
Sotirios Losidis ◽  
Konstadinos Politis
Keyword(s):  
Renewal Process ◽  
Stationary Case ◽  
Recurrence Times ◽  
Ordinary Case

Joint simulation of backward and forward recurrence times in a renewal process

1989 ◽  
Vol 26 (02) ◽  
pp. 404-407 ◽  
Author(s):  
B. B. Winter
Keyword(s):  
Renewal Process ◽  
Joint Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Recurrence Times ◽  
Joint Simulation

It is shown that, in a renewal process with inter-arrival distributionF,an observation from the asymptotic (whent→∞) joint distribution of backward and forward recurrence times attcan be simulated by simulating an observation of the pair (UW, (1 –U)W), whereUandWare independent random variables withU~ uniform(0, 1) andWdistributed according to the length-biased version ofF.

Recurrence processes

1984 ◽  
Vol 21 (1) ◽  
pp. 167-172 ◽  
Author(s):  
Peter McCullagh
Keyword(s):  
Renewal Process ◽  
Recurrence Times ◽  
Subsequent Event

A recurrence process is the process of forward recurrence times from the points of one renewal process to the next subsequent event in a second independent renewal process. Univariate and multivariate recurrence processes are examined. Exponential recurrence processes are investigated in greater detail.

An infinite variance solidarity theorem for Markov renewal functions

1996 ◽  
Vol 33 (2) ◽  
pp. 434-438 ◽  
Author(s):  
M. S. Sgibnev
Keyword(s):  
Renewal Process ◽  
Expected Value ◽  
Infinite Variance ◽  
Markov Renewal Process ◽  
Initial Moment ◽  
Recurrence Times ◽  
The Mean

Let , be a recurrent Markov renewal process and Mik(t) be the expected value of Nk(t) provided that at the initial moment the system is in state i. It is shown that when the mean recurrence times μ ii are finite, the differences μ ij Mki (t) – t behave asymptotically the same for all states i and k.

An infinite variance solidarity theorem for Markov renewal functions

1996 ◽  
Vol 33 (02) ◽  
pp. 434-438 ◽  
Author(s):  
M. S. Sgibnev
Keyword(s):  
Renewal Process ◽  
Expected Value ◽  
Infinite Variance ◽  
Markov Renewal Process ◽  
Initial Moment ◽  
Recurrence Times ◽  
The Mean

Let , be a recurrent Markov renewal process and Mik (t) be the expected value of Nk (t) provided that at the initial moment the system is in state i. It is shown that when the mean recurrence times μ ii are finite, the differences μ ij Mki (t) – t behave asymptotically the same for all states i and k.

Recurrence processes

1984 ◽  
Vol 21 (01) ◽  
pp. 167-172
Author(s):  
Peter McCullagh
Keyword(s):  
Renewal Process ◽  
Recurrence Times ◽  
Subsequent Event

A recurrence process is the process of forward recurrence times from the points of one renewal process to the next subsequent event in a second independent renewal process. Univariate and multivariate recurrence processes are examined. Exponential recurrence processes are investigated in greater detail.

A characterization of the Poisson process using forward recurrence times

1975 ◽  
Vol 78 (3) ◽  
pp. 513-516 ◽  
Author(s):  
Valerie Isham ◽  
D. N. Shanbhag ◽  
M. Westcott
Keyword(s):  
Distribution Function ◽  
Poisson Process ◽  
Real Line ◽  
Renewal Process ◽  
Recurrence Time ◽  
Recurrence Times ◽  
Arithmetic Distribution ◽  
Image Position ◽  
Forward Recurrence Time

Consider a renewal process on the nonnegative real line with non-arithmetic distribution function F(x). Denote by V(x; t) the distribution function of the forward recurrence time from t, t ≤ 0. If t is chosen at random with distribution function Ф(t), the corresponding unconditional forward recurrence time has distribution function

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