By traditional method of large deviations,we obtain the logarithmic asymptotic for the probabilities and large deviation principle for the corresponding measures.

In this article,we studied the large deviation principle and moderate deviation principle for(m-dependent) random variables and φ-mixing random variables.

Under mild conditions,we prove large deviation principles for { ξ λ;λ∈Λ },which generalizes Kifers results.

A regularized strategy which is based on the Gauss kernel is recommened,and the discrepancy principle to select the regularized parameter is proved.

In this article,we studied the large deviation principle and moderate deviation principle for(m-dependent) random variables and φ-mixing random variables.

For the methods of selecting regularization parameter, we will summarize two here: Morozov discrepancy principle and the L curve criterion.

A Posteriori Choice Strategies based on Morozov discrepancy principle is adopted in order to choose the Optimum Regularization Parameter in the Inverse Algorithm of the Photon Correlation Spectroscopy particle sizing techniques.

For linear ill-posed problems,the paper presents a fast convergent method of iterated regularization based on the idea of Landweber iterated regularization,and a method of a-posteriori choice by the Morozov discrepancy principle,by which the optimum asymptotic convergence order of the regularized solution is obtained.