We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We consider a generalized memoryless property which relates to Cantor's second functional equation, study its properties and demonstrate various examples.
Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
References
1
1.Aczel, J. & Dhombres, J. (1989). Functional equations in several variables. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
2
2.Boxma, O., Perry, D., Stadje, W., & Zacks, S. (2006). A Markovian growth-collapse model. Advances in Applied Probability, 38(1): 221–243.CrossRefGoogle Scholar
3
3.Davis, M.H.A. (1993). Markov models and optimization, vol. 49 of Monographs on statistics and applied probability. London: Chapman & Hall.Google Scholar
4
4.Ethier, S.N. & Kurtz, T.G. (1986). Markov processes. Characterization and convergenceWiley series in probability and mathematical statistics. New York: John Wiley & Sons.CrossRefGoogle Scholar
6.Kella, O. & Stadje, W. (2001). On hitting times for compound Poisson dams with exponential jumps and linear release rate. Journal of Applied Probability, 38(3): 781–786.CrossRefGoogle Scholar
7
7.Kijima, M. (1989). Some results for repairable systems with general repair. Journal of Applied Probability26: 89–102.CrossRefGoogle Scholar
8
8.Löpker, A. & Stadje, W. (2011). Hitting times and the running maximum of Markovian growth-collapse processes. Journal of Applied Probability48(2): 295–312.CrossRefGoogle Scholar
9
9.Rao, B.R. & Talwalker, S. (1990). Setting the clock back to zero property of a family of life distributions. Journal of Statistical Planning and Inference24: 347–352.CrossRefGoogle Scholar