Electronic Journal of Probability

An invariance principle for Brownian motion in random scenery

Yu Gu and Guillaume Bal

Full-text: Open access

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.

Article information

Source
Electron. J. Probab., Volume 19 (2014), paper no. 1, 19 pp.

Dates
Accepted: 2 January 2014
First available in Project Euclid: 4 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1465065643

Digital Object Identifier
doi:10.1214/EJP.v19-2894

Mathematical Reviews number (MathSciNet)
MR3164754

Zentralblatt MATH identifier
1286.60081

Subjects
Primary: 60J65: Brownian motion [See also 58J65]
Secondary: 60F17: Functional limit theorems; invariance principles 60F05: Central limit and other weak theorems

Keywords
weak convergence random media central limit theorem

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Gu, Yu; Bal, Guillaume. An invariance principle for Brownian motion in random scenery. Electron. J. Probab. 19 (2014), paper no. 1, 19 pp. doi:10.1214/EJP.v19-2894. https://projecteuclid.org/euclid.ejp/1465065643


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References

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