STRONG APPROXIMATION FOR MOVING AVERAGE PROCESSES UNDER DEPENDENCE ASSUMPTIONS

【摘要】 <正>Let {X_t,t≥1} be a moving average process defined by X_t=sum from k=o to∞akξ_t-k, where {a_k,k≥0} is a sequence of real numbers and {ξ_t,-∞<t<∞} is a doubly infinite sequence of strictly stationary dependent random variables.Under the conditions of {a_k,k≥0} which entail that {X_t,t≥1} is either a long memory process or a linear process,the strong approximation of {X_t,t≥1} to a Gaussian process is studied.Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.更多还原

【Abstract】 Let {X_t,t≥1} be a moving average process defined by X_t=sum from k=o to∞akξ_t-k, where {a_k,k≥0} is a sequence of real numbers and {ξ_t,-∞<t<∞} is a doubly infinite sequence of strictly stationary dependent random variables.Under the conditions of {a_k,k≥0} which entail that {X_t,t≥1} is either a long memory process or a linear process,the strong approximation of {X_t,t≥1} to a Gaussian process is studied.Finally, the results are applied to obtain the strong approximation of a long memory process to a fractional Brownian motion and the laws of the iterated logarithm for moving average processes.更多还原