Abstract
In this article, we propose a denoising algorithm to denoise a time series y i = x i + e i , where {x i } is a time series obtained from a time-T map of a uniformly hyperbolic or Anosov flow, and {e i } a uniformly bounded sequence of independent and identically distributed (i.i.d.) random variables. Making use of observations up to time n, we create an estimate of x i for i < n. We show under typical limiting behaviours of the orbit and the recurrence properties of x i , the estimation error converges to zero as n tends to infinity with probability 1.
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