On Growth-Collapse Processes with Stationary Structure and Their Shot-Noise Counterparts

On growth collapse processes with stationary structure and their shot-noise counterparts

In this paper we generalize existing results for the steady state distribution of growth collapse processes. We begin with a stationary setup with some relatively general growth process and observe that under certain expected conditions point and time stationary versions of the processes exist as well as a limiting distribution for these processes which is independent of initial conditions and ...

Non-stationary synaptic conductances modeled by filtered shot noise processes

We have investigated key statistical properties of systems that can be described by the filtering of shot noise in­ put through a first-order Ordinary Di↵erential Equation (ODE) with variable coe cients. Such systems give rise to filtered shot noise processes with multiplicative noise. Filtered shot noise processes have proven to be very e↵ective in modelling the evolution of systems exposed to...

Shot Noise Cox Processes

On some tractable growth collapse processes with renewal collapse epochs

In this paper we generalize existing results for the steady state distribution of growth collapse processes with independent exponential inter-collapse times to the case where they have a general distribution on the positive real line having a finite mean. In order to compute the moments of the stationary distribution, no further assumptions are needed. However, in order to compute the stationa...

Catastrophe Insurance Modelled with Shot-noise Processes

Shot-noise processes generalize compound Poisson processes in the following way: a jump (the shot) is followed by a decline (noise). This constitues a useful model for insurance claims in many circumstances: claims due to natural catastrophes or self-exciting processes exhibit similar features. We give a general account of shotnoise processes with time-inhomogeneous drivers and derive a number ...