An invariance principle for Brownian motion in random scenery
Yu Gu, Guillaume Bal
TL;DR
This paper establishes an invariance principle for Brownian motion in Gaussian or Poissonian random scenery, providing asymptotic limits across all dimensions with a focus on the novel case of two dimensions.
Contribution
It introduces a new invariance principle for Brownian motion in random scenery, especially addressing the challenging two-dimensional case.
Findings
Derived annealed asymptotic limits in all dimensions
Focused analysis on the two-dimensional case
Used characteristic functions method for proof
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 , which is the main new contribution of the paper.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Point processes and geometric inequalities