【摘要】 设随机序列{X_n; n=0,±1…}可表示成为X_n=sum from j=-∞ to +∞(α_j-nζ_j其中{α_j}是满足sum from j=-∞ to +∞（α_j²）<∞的实数列,{ζ_j}是白噪声序列。通常用（?）_N（λ）=integral from 0 to λ（1/2πN）∣sum from k=1 to N(x_?e^iμk∣² dμ来估计{x_n}的未知的谱函数F（λ）。在一定的条件下,当{ζ_j}是独立同分布随机序列时,和[3]证明了:过程√（?）[（?）_N（λ）-F（λ）]的分布弱收敛到某个正态过程ζ（λ）在C[0,π]上产生的测度。本文在他们工作的基础上,运用鞅的极限定理和鞅不等式,改进了[3]中的两个关键引理,从而证明了当{ζ_j}是有控制分布的实四阶鞅差序列时,仍有相同的结果。更多还原

【Abstract】 We consider a real stochastic process(xn,n= 0,±1,…),xn= ,where{aj}is areal sequence with is white noise, Usually,is used as estimate for the unknown spectral function F(γ).When{ξj} is a i.i.d.random sequence and [3]proved that under certain conditions,the measures PN in C[0,π]generated by the processes weakly converge to the measur P in C[0,π] generated by some Gaussian process. In this paper, we prove that the same result is also true when {ξj} is a real fourth-order martingale difference sequence with controlled distribution.Therefore,their result is extended.更多还原