Asymptotic Study Of A Class Of Random Walk Models With Feedback Mechanism

This thesis mainly to generalize Elephant random walk(ERW)model and Elephan-t random walk with delays(ERWD)model respectively,and the method of Gut and Stadtmuller[10]is used to study the asymptotic properties of the extended model respec-tively.First of all,The feedback mechanism of ERW model is generalized,the feedback mechanism only reports the motion of {X1,X2,Xn-1,Xn,} at time n+1.Second,The feedback mechanism of ERWD model is generalized,the feedback mechanism only reports the motion of {X1,Xn-1,Xn,} at time n+1.In the end,The traveling process of the particle {(?)} is analyzed,the asymptotic normality of ERW model and ERWD model is obtained by using the difference equation to solve the expectation and variance.