Abstract
In this paper we study a problem of preserving the probabilistic and statistic properties of the random walks under sample space mapping, in particular, under mapping of random walk sample space into the space of sufficient statistics of that random walk. We consider problems of closedness and completeness of the random walk’s plans, formulate necessary conditions of the mapped plan’s completeness, consider the problem of constructing an unbiased estimate for a function of unknown parameter, and find an unbiased estimate for the probability density of getting into a reachable area.
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