Document Zbl 1286.60081

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An invariance principle for Brownian motion in random scenery. (English) Zbl 1286.60081

Electron. J. Probab. 19, Paper No. 1, 19 p. (2014).

Summary: 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.

Cited in 2 Documents

MSC:

60J65	Brownian motion
60K37	Processes in random environments
60F17	Functional limit theorems; invariance principles
60F05	Central limit and other weak theorems

Keywords:

weak convergence; random media; central limit theorem

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