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In this paper, we formulate a stochastic logistic fish growth model driven byboth white noise and non-Gaussian noise. We focus our study on the mean time toextinction, escape probability to measure the noise-induced extinctionprobability and the Fokker-Planck equation for fish population X(t). In theGaussian case, these quantities satisfy local partial differential equationswhile in the non-Gaussian case, they satisfy nonlocal partial differentialequations. Following a discussion of existence, uniqueness, and stability, wecalculate numerical approximations of the solutions of those equations. Foreach noise model we then compare the behaviors of the mean time to extinctionand the solution of the Fokker-Planck equation as growth rate r, carryingcapacity K, the intensity of Gaussian noise ${\lambda}$, noise intensity${\sigma}$ and stability index ${\alpha}$ vary. The MET from the interval (0,1)at the right boundary is finite if ${\lambda} <{\sqrt2}$. For ${\lambda} >{\sqrt2}$, the MET from (0,1) at this boundary is infinite. A larger stabilityindex ${\alpha}$ is less likely to lead to the extinction of the fishpopulation.

Mean Exit Time and Escape Probability for the Stochastic Logistic Growth Model with Multiplicative {\alpha}-Stable L\'evy Noise