# Integration of the stochastic logistic equation via symmetry analysis

## TL;DR

This paper uses symmetry analysis to explicitly solve a stochastic logistic equation, providing a formula that relates the solution directly to the Wiener process driving the stochasticity.

## Contribution

It introduces a novel application of symmetry methods to integrate stochastic differential equations explicitly, specifically for the logistic model.

## Key findings

- Derived an explicit solution formula for the stochastic logistic equation.
- Demonstrated the effectiveness of symmetry analysis in stochastic differential equations.
- Provided insights into the structure of solutions for stochastic population models.

## Abstract

We apply the recently developed theory of symmetry of stochastic differential equations to a stochastic version of the logistic equation, obtaining an explicit integration, i.e. an explicit formula for the process in terms of any single realization of the driving Wiener process.