An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise

TL;DR

This paper derives an exact analytical solution for generalized growth models with stochastic growth rates driven by Markovian dichotomic noise, applicable across various scientific fields.

Contribution

It provides the first exact solution for growth models influenced by asymmetric Markovian dichotomic noise, enhancing understanding of stochastic growth processes.

Findings

Exact probability distribution derived for the growth model.

Applicable to diverse fields like biology, astrophysics, and laser physics.

Offers a new analytical tool for stochastic growth analysis.

Abstract

Logistic growth models are recurrent in biology, epidemiology, market models, and neural and social networks. They find important applications in many other fields including laser modelling. In numerous realistic cases the growth rate undergoes stochastic fluctuations and we consider a growth model with a stochastic growth rate modelled via an asymmetric Markovian dichotomic noise. We find an exact analytical solution for the probability distribution providing a powerful tool with applications ranging from biology to astrophysics and laser physics.