Integration of the stochastic logistic equation via symmetry analysis

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.

arXiv commentpreprint version; final version to appear in J Nonlin Math Phys

References in corpus (6)

• Correlated noise in a logistic growth model
• Population extinction in a fluctuating environment
• Symmetry of stochastic non-variational differential equations
• Ecological Complex Systems
• Random Lie-point symmetries of stochastic differential equations
• Asymptotic regime in N random interacting species

Cited by in corpus (4)

• Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
• Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field
• Integrable Ito equations with multiple noises
• Asymptotic symmetry and asymptotic solutions to Ito stochastic differential equations