有限相依随机过程的Cramér定理

CRAMER'S THEOREM FOR m-DEPENDENT RANDOM PROCESSES

设ζ_1ζ_n(n≥1)是i.i.d.实值随机变量,a_1,…,a_m是一组实数。定义X_a=sum from i=1 to (?) (a_iζ_i+a,(?)=1/n sum from i=1 to n (X_a)。)本文证明:若Eexp(tζ)<∞(A|t|<η),则服从大偏差原理。

Let n>l,be i. i. d. real valued random variables with Eexp(t)< for t in some neighborhood of 0. Let a1,... , am be real numbers. Define We prove that satisfies the large deviation principle.