Using maximum cross section method for filtering jump-diffusion random processes

The paper is focused on problem of filtering random processes in dynamical systems whose mathematical models are described by stochastic differential equations with a Poisson component. The solution of a filtering problem supposes simulation of trajectories of solutions to a stochastic differential equation. The trajectory modelling procedure includes simulation of a Poisson flow permitting application of the maximum cross section method and its modification.

Effect of covariate misspecifications in the marginalized zero-inflated Poisson model

Count outcomes are often modelled using the Poisson regression. However, this model imposes a strict mean-variance relationship that is unappealing in many contexts. Several studies in the life sciences result in count outcomes with excessive amounts of zeros. The presence of the excess zeros introduces extra dispersion in the data which cannot be accounted for by the traditional Poisson regression. The zero-inflated Poisson (ZIP) and zero-inflated negative binomial models are popular alternative. The zero-inflated models comprise two key components; a logistic part which models the zeros, and a Poisson component to handle the positive counts. Both components allow the inclusion of covariates. Civettini and Hines [

A STOCHASTIC CLEARING MODEL WITH A BROWNIAN AND A COMPOUND POISSON COMPONENT

We consider a stochastic input–output system with additional total clearings at certain random times determined by its own evolution (and specified by a controller). Between two clearings, the stock level process is a superposition of a Brownian motion with drift and a compound Poisson process with positive jumps, reflected at zero. We introduce meaningful cost functionals for this system and determine them explicitly under several (classical and new) clearing policies.