Non‐Markov noise processes

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...

Point Processes Observed with Noise

Noise processes in nanomechanical resonators

Nanomechanical resonators can be fabricated to achieve high natural resonance frequencies, approaching 1 GHz, with quality factors in excess of 10. These resonators are candidates for use as highly selective rf filters and as precision on-chip clocks. Some fundamental and some nonfundamental noise processes will present limits to the performance of such resonators. These include thermomechanica...

Complex determinantal processes and H noise

For the plane, sphere, and hyperbolic plane we consider the canonical invariant determinan-tal point processes Z ρ with intensity ρdν, where ν is the corresponding invariant measure. We show that as ρ → ∞, after centering, these processes converge to invariant H 1 noise. More precisely, for all functions f ∈ H 1 (ν) ∩ L 1 (ν) the distribution of z∈Z f (z) − ρ π f dν converges to Gaussian with m...