Microscopic fluctuation theory (mFT) for interacting Poisson processes

Exact Statistical Inference for Some Parametric Nonhomogeneous Poisson Processes

Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametri...

Self-consistent microscopic theory of fluctuation-induced transport.

A Maxwell’s demon type “information engine” that extracts work from a bath is constructed from a microscopic Hamiltonian for the whole system including a subsystem, a thermal bath, and a nonequilibrium bath of phonons or photons that represents an information source or sink. The kinetics of the engine is calculated self-consistently from the state of the nonequilibrium bath, and the relation of...

Interacting Poisson Processes and Applications to Neural Modeling

We introduce a modification of the classical Hawkes’ processes in which also inhibitory connections between units are allowed. This formalism is used to model networks of neurons characterized by an exponential transfer function. The expected intensities of the process are approximated by a differential system of first-order and the stability of the solutions of this equation is studied. We dis...

Fluctuation Theory and Stochastic Games for Spectrally Negative Lévy Processes

Poisson Processes for Neuroscientists

This note is an introduction to the key properties of Poisson processes, which are extensively used to simulate spike trains. For being mathematical idealizations, Poisson processes rely on some simplifying assumptions that limit their scope of application. The best way to understand these limitations is perhaps by constructing the Poisson process gradually starting from the intuitively clear s...