| A GARCH(1,1) model is defined aswith initial values y0≥0 and h0≥0 a.s., where ω>0 ,a ≥0 ,b≥0 and {η,ηt, t≥1}is a sequence of independent and identically distributed random variables.When the model is nonstationary, that is Elogb(b+aη2)≥0 , under suitable moment conditions or tailed probability conditions, the Marcinkiewicz-Zygmund strong (weak)law of large numbers and Hartmann-Winter law of the iterated logarithm, the generalized central limit theorem and the corresponding Chover law of the iterated logarithm are obtained. And the simulations are given for the Marcinkiewicz-Zygmund strong law of large numbers. |
