Killed stable kernels and the Markov property of the excursion measure

Main results:

• killedStableKernel: the stable kernel killed at its first strict passage below zero.
• excursion_markov_lintegral, excursion_markov_integral: the Markov property of the excursion measure at a positive age, for nonnegative and for integrable test functions.
• excursion_remainingLifetime_lintegral: the remaining lifetime is a stable passage time.
• N_noFixedJump: the excursion measure has no fixed jump times.
• exists_excursionAge_stoppingTimes: strict age-window clocks that are stopping times.
• lastPositiveTime bridges: the lifetime of an excursion future is its last positive time.

References

• J. Bertoin, Lévy Processes, Cambridge University Press, 1996, Chapter IV.
• T. Duquesne and J.-F. Le Gall, Random Trees, Lévy Processes and Spatial Branching Processes, Astérisque 281 (2002), Chapter 1.