The Limit Distribution Of An Inhomogeneous One-dimensional Logistic Model

In this thesis,the limit distribution of the real Logistic model X_tis studied by using the exact moment estimation and recursive relation.Based on the one-dimensional Logistic model,the constant part of the equation is generalized as a general parameter to determine the research model X_t.Then the exact p-order moment EX_t~pis bounded by using one-dimensional Ito formula,H¨older inequality,etc.The concrete form of the moment EX_t~pis obtained by the recursive relations among each p-order moment.Finally,the lemma Carleman condition is verified to get the main conclusion of this thesis:the limit distribution of X_texists and is unique.The model X_tstudied in this thesis is different from the general one-dimensional Logistic model.Instead,in the model X_t,the constants in the basic model are general-ized as general parameters,and some parameters are no longer strictly required to be constants.Therefore,the model X_tis more widely used in real life.