Information recovery from observations by a random walk having jump\n distribution with exponential tails

2011/10/31 by Andrew Hart, Hart, Andrew, Fábio P. Machado +3
Computer Science · Mathematics · #60G50 #60K37 #Bayesian Methods and Mixture Models #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1110.6853

openalex publication_date 2011/10/31 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

A it scenery is a coloring \ξ of the integers. Let S_{t t\≥ 0}\nbe a recurrent random walk on the integers. Observing the scenery \ξ along\nthe path of this random walk, one sees the color \χ_t:=\ξ(S_t) at time\nt. The it scenery reconstruction problem is concerned with recovering the\nscenery \ξ, given only the sequence of observations \χ:=(\χ_t)_t\≥\n0. The scenery reconstruction methods presented to date require the random\nwalk to have bounded increments. Here, we present a new approach for random\nwalks with unbounded increments which works when the tail of the increment\ndistribution decays exponentially fast enough and the scenery has five colors.\n

Citations

• Reconstructing a two-color scenery by observing it along a simple random walk path

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