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The quenched limiting distributions of a one-dimensional random walk in random scenery

2013; Institute of Mathematical Statistics; Volume: 18; Issue: none Linguagem: Inglês

10.1214/ecp.v18-2918

1083-589X

Nadine Guillotin‐Plantard, Yueyun Hu, Bruno Schapira,

Markov Chains and Monte Carlo Methods

For a one-dimensional random walk in random scenery (RWRS) on Z, we determine its quenched weak limits by applying Strassen's functional law of iterated logarithm. As a consequence, conditioned on the random scenery, the one dimensional RWRS does not converge in law, in contrast with the multi-dimensional case.