Abstract：Let {Xn,n ≥ 1} be a strictly stationary φ-mixing sequence, {Nn,n ≥ 1} be a sequence of nonnegative integer valued random variable. Note SNn=Xi be the random partial sums, we prove the random central limit theorem for strictly stationary φ-mixing sequence using the limit properties of φ-mixing sequence under some suitable conditions, and obtain that Xn=(SNn-ESNn)/√(Var(SNn)) converges to T(Z1,Z2), where T(Z1,Z2) is the linear function of Z1 and Z2, Z1~N(0,1), Z2 is the limit distribution after normalization of Nn,n ≥ 1.
邢峰, 邹广玉. φ-混合序列的随机中心极限定理[J]. 浙江大学学报（理学版）, 2018, 45(4): 413-415.
XING Feng, ZOU Guangyu. The random central limit theorem for φ-mixing sequence.. Journal of ZheJIang University(Science Edition), 2018, 45(4): 413-415.
[1] LIN Z Y, LU C R. Limit Theory for Mixing Dependent Random Variables[M]. Beijing:Science Press/Kluwer Academic Publishers, 1997.
[2] IBRAGIMOV I A. Some limit theorems for stationary processes[J]. Akademija Nauk SSSR Teorija Verojatnoste1iee Primenenija, 1962(7):361-392.
[3] PRAKASA RAO B L S. Remark on the rate of convergence in the random central limit theorem for mixing sequences[J]. Z Wahrscheinlichkeitstheorie Und Verw Gebiete, 1975, 31(2):157-160.
[4] LEE S. Random central limit theorem for the linear process generated by a strong mixing process[J].Statistics & Probability Letters, 1997,35(2):189-196.
[5] 谭希丽, 杨晓云. B值m相依随机元序列的随机指标中心极限定理[J].吉林大学学报(理学版), 2003, 41(4):419-430. TAN X L, YANG X Y. The central limit theorem for the sum of a random number of m-dependent B-valued random variables[J]. Journal of Jilin University (Science Edition), 2003, 41(4):419-430.
[6] 谭希丽, 杨晓云. B值m相依随机元列移动平均过程的随机指标中心极限定理[J]. 吉林大学学报(理学版), 2007, 45(2):159-164. TAN X L, YANG X Y. The central limit theorem for the sum of a random number of moving average processes of m-dependent B-valued elements[J]. Journal of Jilin University (Science Edition), 2007, 45(2):159-164.
[7] HWANG E, SHIN D W. Random central limit theorems for linear processes with weakly dependent innovations[J]. Journal of the Korean Statistical Society, 2012, 41(3):313-322.
[8] PRAKASA RAO B L S, SREENHARI M. Random central limit theorem for associated random variables and the order of approximation[J]. Statistics & Probability Letters, 2016, 111:1-7.
[9] BILLINGSLEY P. Convergence of Probability Measures[M]. New York:Wiley, 1968.
2018, Vol. 45 
Xi，在适当的假设条件下，利用φ混合序列的极限性质，证明了严平稳φ混合序列的随机中心极限定理，得到了Xn=（SNn-ESNn）/√
Xi be the random partial sums, we prove the random central limit theorem for strictly stationary φ-mixing sequence using the limit properties of φ-mixing sequence under some suitable conditions, and obtain that Xn=(SNn-ESNn)/√