Limiting Behavior of A Sequence of Density Ratios
Let X1, X2,"¦.. be a sequence of random variables and Ð = {Pθ,θ Є (-)} be a family of distributions of the sequence. For each n, An is the σ-field generated by X1,"¦, Xn.If θ1,θ2 Є (-), we define Rn (θ1,θ2) as the density ratio of Pθ1,Pθ2 on An.The main purpose of the paper is to investigate limiting behavior of the sequence Rn with respect to any Pθ. This has applications in sequential analysis, where it is desired to know whether a sequential probability ratio test terminates with probability one. The same conclusion can be drawn in the case of generalized sequential probability…





