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Sequential inferences with prescribed accuracy for semimartingales. (English. Russian original) Zbl 0693.62066

Theory Probab. Appl. 33, No. 3, 446-459 (1988); translation from Teor. Veroyatn. Primen. 33, No. 3, 480-494 (1988).
We consider a number of sequential procedures with prescribed accuracy relative to the parameter of random processes with continuous and discrete time having a semimartingale structure. We propose a general semimartingale model of an observable process that permits us to study sequential procedures from a unified standpoint.
A description of this model and a number of general definitions are given in § 2. In § 3 we examine pointwise sequential estimates for the parameter appearing linearly in the drift of an observable square- integrable semimartingale, and adduce a number of examples. We also discuss the efficiency of the considered sequential estimates. In § 3 we construct confidence intervals and sequential criteria for distinguishing hypotheses about the drift of an observable square- integrable semimartingale. In the same section we also examine the case of nonsquare-integrable martingales.

MSC:

62L12 Sequential estimation
62M05 Markov processes: estimation; hidden Markov models
60G48 Generalizations of martingales
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