Markov random walks in the space of a sufficient statistic and statistical inference (Q1269941)

Sequential schemes of observations play an important role in the modern theory of statistical inference. In these schemes, the time at which observations are terminated is a random variable. Sequential schemes were proposed by \textit{A. Wald} [Sequential analysis. (1947; Zbl 0029.15805)] and, based on the likelihood ratio, were oriented to testing hypotheses. This direction of sequential analysis is well known. Another important direction of sequential analysis based on the plans of random walks turned out to attract less attention. The aim of this review is to describe the models of sequential analysis based on the plans of random walks. Here we consider some results concerning the models of random walks. Much attention will be paid to the research concerning the construction of random walk models performed at Perm State University in 1970-1995 by Ya. P. Lumel'skij, Ya. M. L'vovskij, S. I. Frolov, E. G. Tsylova, V. V. Chichagov, and others.