| Abstract: | In this paper we analyse Markov-modulated fluid processes over finite time intervals. We study the joint distribution of the level at time (theta < infty ) and of the maximum level over [0, θ], as well as the joint distribution of the level at time θ and the minimum level over [0, θ]. We approximate θ by a random variable T with Erlang distribution and so use an approach different from the usual Laplace transform to compute the distributions. We present probabilistic interpretation of the equations and provide a numerical illustration. |
