The Application Of Stein's Method On Embedding Theorem

In the paper,we study embedding theorem on a series of log-concave distri-butions and its index moment estimation.This paper applies Stein's method and fixed point theorem on convex compact.First,two bound distributions of random variable are obtained by Stein's equality.Next,two bound distributions of random variable consist of joint distribution of random variable and its infinitesimal oper-ator;Finally this paper uses Stein's equality of joint distribution to achieve index moment estimation of two bound distributions.With these methods,when random variable meets log-concave distribution and Stein's equality,this paper makes the index moment estimation of joint distribution approximated to formate embedding theorem on log-concave distribution.