Abstract
A growth-collapse process is one which grows linearly between random partial collapse times. The jump down of the process at a collapse time has a random size, following some distribution which is conditional on the level of the process at that time. There are many application of such models in geophysics, population growth, insurance models, inventory systems, and more.
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References
Boxma, O. Perry, D. Stadje, W. and Zacks, S. (2006). A Markovian Growth-Collapse Model, Adv. Appl. Prob. 38:221–243.
Perry, D., Stadje, W. and Zacks, S. (2007). Hysteretic capacity switching for M/G/1 queues. Stochastic Models, 23:277–305.
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Zacks, S. (2017). Miscellaneous Topics. In: Sample Path Analysis and Distributions of Boundary Crossing Times. Lecture Notes in Mathematics, vol 2203. Springer, Cham. https://doi.org/10.1007/978-3-319-67059-1_9
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DOI: https://doi.org/10.1007/978-3-319-67059-1_9
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