A note on general sliding window processes

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A note on general sliding window processes

Let f : R → [r] = {1, 2, . . . , r} be a measurable function, and let {Ui}i∈N be a sequence of i.i.d. random variables. Consider the random process Zi = f(Ui, ..., Ui+k−1). We show that for all q, there is a positive probability, uniform in f , that Z1 = Z2 = ... = Zq. A continuous counterpart is that if f : R → R, and Ui and Zi are as before, then there is a positive probability, uniform in f ...

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ژورنال

عنوان ژورنال: Electronic Communications in Probability

سال: 2014

ISSN: 1083-589X

DOI: 10.1214/ecp.v19-3341