STABILITY ANALYSIS AND PARAMETER ESTIMATION OF A STOCHASTIC LOGISTIC GROWTH MODEL WITH MULTIPLICATIVE α-STABLE LÉVY NOISE

Since the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations(SDEs) that are driven not only by Brownian motion but also by α-stable Lévy noises are more appropriate to model such statistical behavior of non-Gaussian processes with heavy-tailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes defined as solutions to stochastic logistic differential equations driven by multiplicative α-stable Lévy noise. We mainly focus on one-dimensional stochastic logistic jump-diffusion processes driven by Brownian motion and α-stable Lévy motion. First, we present the stability analysis of the solution of a stochastic logistic growth model with multiplicative α-stable Lévy. We establish the existence of a unique global positive solution of this model under certain conditions. Then, we find the sufficient conditions for the almost sure exponential stability of the trivial solution of the model. Next, we provide parameter estimation for the proposed model. In parameter estimation, we use statistical methods to get an optimal and applicable estimator. We also investigate the consistency and asymptotics of the proposed estimator. We assess the validity of the estimators with a simulation study.