Asymptotic analysis of Poisson shot noise processes, and applications

Nonstationary filtered shot-noise processes and applications to neuronal membranes.

Filtered shot noise processes have proven to be very effective in modeling the evolution of systems exposed to shot noise sources and have been applied to a wide variety of fields ranging from electronics through biology. In particular, they can model the membrane potential V(m) of neurons driven by stochastic input, where these filtered processes are able to capture the nonstationary character...

Shot Noise Cox Processes

Generalised Shot Noise Cox Processes

We introduce a new class of Cox cluster processes called generalised shotnoise Cox processes (GSNCPs), which extends the definition of shot noise Cox processes (SNCPs) in two directions: the point process which drives the shot noise is not necessarily Poisson, and the kernel of the shot noise can be random. Thereby a very large class of models for aggregated or clustered point patterns is obtai...

Crossings of smooth Shot Noise Processes

In this paper, we consider smooth shot noise processes and their expected number of level crossings. When the kernel response function is sufficiently smooth, the mean number of crossings function is obtained through an integral formula. Moreover, as the intensity increases, or equivalently as the number of shots becomes larger, a normal convergence to the classical Rice’s formula for Gaussian ...

Tail Behavior of Shot Noise Processes

We discuss the diierent ways heavy tails can arise in shot noise models and possible applications of the latter to nancial modeling.