Die waldsche fundamentalidentität und ein sequentieller quotiententest für eine zufäallige irrfahrtüber einer homogenen irreduziblen markovschen kette mit endlichem zustandsraum

Abstract

For a random walk {R n ≥0} given on a homogeneous irreducible finite MARKOV chain {X n ≥0} the identity (8) is obtained. Generalizations (14)-(16) of WALD's Fundamental Identity and WALD's first and second equations for the two-dimensional process {(R n ,X n ), n≥0} are proved. The Average Sample Number (21)-(22) and the Operating Characteristic Function (24)-(25) of a Sequential Probability Ratio Test follow. With this test a decision about two simple hypotheses on the unknown transition probability matrix of {X n , n≥0} and the unknown parameters of the probability distributions for the increments of {X n , n≥0} can be made. For a special case these results were proved by PHATARFOD [6] and KuCHLER [3] with other methods.