Dissipative stochastic evolution equations driven by general Gaussian and non-Gaussian noise

TL;DR

This paper investigates a broad class of stochastic evolution equations with dissipative nonlinearities driven by both Gaussian and non-Gaussian noises, including fractional Brownian motion and Hermite processes, with applications to modeling potential spread in dendritic trees.

Contribution

It introduces a unified framework for analyzing stochastic evolution equations driven by general Gaussian and non-Gaussian noises, extending existing models to include long-range dependence.

Findings

Established existence and uniqueness results for the equations.

Demonstrated applicability to models of potential spread in dendritic trees.

Extended the analysis to include processes with long-range dependence.

Abstract

We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers examples of Gaussian processes, like fractional and bifractional Brownian motion and also non Gaussian examples like the Hermite process. We give an application of our results to the study of the stochastic version of a common model of potential spread in a dendritic tree. Our investigation is specially motivated by possibility to introduce long-range dependence in time of the stochastic perturbation.