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We endow the classical stochastic fluid process with a duration-dependentMarkovian arrival process (DMArP). We show that this provides a flexible modelfor the revenue of a solar energy generator. In particular, it allows forheavy-tailed interarrival times and for seasonality embedded into thestate-space. It generalizes the calendar-time inhomogeneous stochastic fluidprocess. We provide descriptors of the first return of the revenue process. Ourmain contribution is based on the uniformization approach, by which we reducethe problem of computing the Laplace transform to the analysis of the processon a stochastic Poissonian grid. Since our process is duration dependent, ourconstruction relies on translating duration form its natural grid to thePoissonian grid. We obtain the Laplace transfrom of the project value based ona novel concept of $n$-bridge and provide an efficient algorithm for computingthe duration-level density of the $n$-bridge. Other descriptors such as theLaplace transform of the ruin process are further provided.

Duration-dependent stochastic fluid processes and solar energy revenue modeling