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First exit times for compound Poisson dams with a general release rule

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Abstract

An infinite dam with compound Poisson inputs and a state-dependent release rate is considered. For this dam, we solve Kolmogorov’s backward differential equation to obtain the Laplace transforms of the first exit times in terms of a certain positive kernel. This allows us to provide an explicit expression for the Laplace transform of the wet period for a finite dam.

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Correspondence to Jiyeon Lee.

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Lee, J. First exit times for compound Poisson dams with a general release rule. Math Meth Oper Res 65, 169–178 (2007). https://doi.org/10.1007/s00186-006-0111-3

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  • DOI: https://doi.org/10.1007/s00186-006-0111-3

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