# A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysis

## TL;DR

This paper introduces a randomized Beverton-Holt discrete model, deriving its probabilistic properties and steady states, supported by numerical examples to illustrate the theoretical findings.

## Contribution

It provides a full probabilistic analysis of a stochastic Beverton-Holt model, including density functions and steady states, which is a novel extension of the classical model.

## Key findings

- Derived the first and second probability density functions of the model
- Identified the random steady state of the stochastic process
- Validated theoretical results with numerical examples

## Abstract

In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density function are obtained by means of the random variable transformation method, providing a full probabilistic description of the solution. Finally, several numerical examples are shown.