The distribution of the supremum for spectrally asymmetric Lévy processes


In this article we derive formulas for the probability IP(supt≤T X(t) > u), T > 0 and IP(supt<∞X(t) > u) where X is a spectrally positive Lévy process with infinite variation. The formulas are generalizations of the well-known Takács formulas for stochastic processes with non-negative and interchangeable increments. Moreover, we find the joint distribution… (More)