Theorems on large deviations for the sum of random number of summands - Kasparavičiūtė, Aurelija; Saulis, Leonas (Lietuvos matematikos rinkinys, 2010)
In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i = 1, 2, . . . with  mean EXi = µ and variance DXi = σ2 > 0. It is assumed that Nt is a non-negative integervalued random variable, which depends on t > 0 and is independent of Xi, i = 1, 2, . . . .
Keywords: cumulant; large deviations; compound Poisson process