2012/03/01 by Hermine Biermé, Agnès Desolneux
Economics, Econometrics and Finance · Mathematics · Decision Sciences · #Stochastic processes and financial applications #Point processes and geometric inequalities #Probability and Risk Models
paper · pdf · doi:10.1017/s0021900200008883
We use a change-of-variable formula in the framework of functions of bounded variation to derive an explicit formula for the Fourier transform of the level crossing function of shot noise processes with jumps. We illustrate the result in some examples and give some applications. In particular, it allows us to study the asymptotic behavior of the mean number of level crossings as the intensity of the Poisson point process of the shot noise process goes to infinity.