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      A self-similar process arising from a random walk with random environment in random scenery

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          Abstract

          In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies.

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            Limit Theorems for Stochastic Processes

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              A limit theorem related to a new class of self similar processes

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                Author and article information

                Journal
                25 February 2011
                Article
                10.3150/09-BEJ234
                1102.5241
                857361c6-f8ea-4903-ba3e-53b5b9371ebb

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                IMS-BEJ-BEJ234
                Bernoulli 2010, Vol. 16, No. 3, 825-857
                Published in at http://dx.doi.org/10.3150/09-BEJ234 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
                math.ST stat.TH
                vtex

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