Overview of normal approximation by steins method is given in rinott and rotar 2000 in the present paper we give a somewhat di erent presentation we pay greater attention on the derivation of the method and highlight a di erent concept of weak dependence a comprehensive presentation of the poisson approximation is given in barbour. Then for any random variable w evaluate the left hand side of the stein equation at w and take the expectation obtaining e w e z the objective of this paper is to introduce the ideas of steins method to the nonlinear case the expected stein equation for g normal distribution would be 12 g f x x 2 f . In this work we use the steins method to obtain a general theorem of non uniform exponential bound on normal approximation base on monotone size bias couplings of w applications of the main . Discrete malliavin stein method berry esseen bounds for random graphs and percolation krokowski kai reichenbachs anselm and thale christoph the annals of probability 2017 a large deviation principle for the erdos renyi uniform random graph dembo amir and lubetzky eyal electronic communications in probability 2018
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