An embedding for the Kesten-Spitzer random walk in random scenery
Endre Csáki, Wolfgang König, Zhan Shi
Abstract
For one-dimensional simple random walk in a general i.i.d. scenery and its limiting process we construct a coupling with explicit rate of approximation extending a recent result for Gaussian sceneries due to Khoshnevisan and Lewis. Furthermore we explicity identify the constant in the law of iterated logarithm.
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