Completeness of the plans of sequential estimation for Wiener spaces with a drift and some uniqueness theorems

One considers a family of n-dimensional Wiener processess x(t) =(t) +t, depending on a drift parameter , where is the standard Wiener process. Let be a closed subset of the space of trajectories ⁿ×₊ (plan) and assume that the measure , defined by the first occurrence of the trajectory of the process x in the set , is a probability measure. One gives conditions which the plan has to satisfy in order that from the equality for any there should follow that f 0.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 126, pp. 69–72, 1983.The authors are grateful to V. P.Khavin for discussions on certain questions of potential theory.