The Asymptotic Behavior of the Mean Sojourn Time for a Random Walk Above a Receding Curvilinear Boundary

2019 ◽  
Vol 237 (4) ◽  
pp. 511-520 ◽  
Author(s):  
I. S. Borisov ◽  
E. I. Shefer
Keyword(s):  
Asymptotic Behavior ◽  
Random Walk ◽  
Sojourn Time ◽  
Curvilinear Boundary ◽  
The Mean ◽  
Mean Sojourn Time

On the asymptotics of the mean sojourn time of a random walk on a semi-axis

2015 ◽  
Vol 79 (3) ◽  
pp. 449-466 ◽  
Author(s):  
V I Lotov ◽  
A S Tarasenko
Keyword(s):  
Random Walk ◽  
Sojourn Time ◽  
The Mean ◽  
Mean Sojourn Time

On the Lead Time of a Periodic Screening Program

1983 ◽  
Vol 22 (01) ◽  
pp. 45-50 ◽  
Author(s):  
Berthold Maier
Keyword(s):  
Lower Bound ◽  
Sojourn Time ◽  
Screening Test ◽  
Initial Phase ◽  
Lead Time ◽  
Screening Program ◽  
The Mean ◽  
Mean Sojourn Time

Many parameters are needed in the assessment of the benefits of a periodic screening program. In this paper we present formulas for two of them: the proportion SP of patients detected and the lead time of such a program. The lead time is the time by which the disease is detected earlier due to screening. We also give a lower bound for the mean lead time L in terms of the mean sojourn time in a certain preclinical state P and of the sensitivity of the screening test in this state P only. Finally, we indicate how the mean sojourn time and, under certain assumptions, even the sensitivity are estimated from the results during the initial phase of the screening program.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

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