具有随机足标的平稳正态序列的部分和与最大值的联合极限分布

On the Joint Limiting Distribution of the Partial Sum and Maximum of Strongly Dependent Stationary Normal Sequence with Random Sample Size

设X1,X2,…为标准化平稳正态序列,相关系数ρ｜i-j｜=EXiXj(i≠j),N(n)为取正整数的随机变量且N(n)nPη,η为大于0的随机变量.得到了:当ρnlogn→γ∈(0,∞)时,最大值MN(n)和部分和SN(n)的联合极限分布.

Let X_1,X_2,... be standardized stationary normal sequences with correlation ρ___(|i-j|)=EX_iX_j(i≠j). Let N(n) be a positive integer valued random variable and N(n)nPη, where η is a positive random variable. The asymptotic joint distribution of M_(N(n)) and S_(N(n)) is derived as ρ_n log n→γ∈(0, ∞).