Moments and probability density of threshold crossing times for populations in random environments under sustainable harvesting policies

Abstract

Stochastic differential equations are used to model the dynamics of harvested populations in random environments. The main goal of this work is to compute, for a particular fish population under constant effort harvesting, the mean and standard deviation of first passage times by several lower and upper thresholds values. We apply logistic or logistic-like with Allee effects average growth dynamics. In addition, we present a method to obtain the probability density function of the first passage time by a threshold through the numerical inversion of its Laplace transform.