Normal approximation for sum of random number of summands

Abstract

Normal aproximationof sum Z_t =Σ^Nt_i=1X_i of i.i.d. random variables (r.v.) X_i , i = 1, 2, . . . with mean EX_i = μ and variance DX_i = σ² > 0 is analyzed taking into consideration large deviations. Here N_t is non-negative integer-valued random variable, which depends on t , but not depends at X_i , i = 1, 2, . . ..