Analysis of diffusive size-structured population model with stochastic perturbation

Abstract

In this work, we introduce a diffusive stochastic size-struc\-tured population model. After formulating the problem in an abstract framework, we derive mild solution to the given model. We show the existence and uniqueness of the mild solution to the given model in a Hilbert space. We use the Burkholder-Davis-Gundy's lemma to prove the uniqueness of the mild solution. We also show that the system is quasi invariant in the second moment and also mean square dissipative.