Benjamin Weiss

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—For a stationary stochastic process {Xn} with values in some set A, a finite word w ∈ A K is called a memory word if the conditional probability of X0 given the past is constant on the cylinder set defined by X −1 −K = w. It is a called a minimal memory word if no proper suffix of w is also a memory word. For example in a K-step Markov processes all words(More)
For a binary stationary time series define σn to be the number of consecutive ones up to the first zero encountered after time n, and consider the problem of estimating the conditional distribution and conditional expectation of σn after one has observed the first n outputs. We present a sequence of stopping times and universal estimators for these(More)