An invariance principle for Brownian motion in random scenery

Yu Gu (Columbia University)
Guillaume Bal (Columbia University)

Abstract


We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$, which is the main new contribution of the paper.


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Pages: 1-19

Publication Date: January 2, 2014

DOI: 10.1214/EJP.v19-2894

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