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A Limit Theorem for Brownian Motion in a Random Scenery

Published online by Cambridge University Press:  20 November 2018

Bruno Remillard  and
Donald A. Dawson
Bruno Remillard
Affiliation:
Département de Mathématiques et d'informatique, U.Q.T.R., Trois Rivières, Québec G9A 5H7
Donald A. Dawson
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6
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Abstract

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We find the limiting distribution of , where {Bu}u≧0 is the standard Brownian motion on ℝd, V is a particular random potential and {an}n≧1 is a normalizing sequence.

Keywords

60J6060F05Weak convergencerandom sceneryBrownian motion
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 385 - 391
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Billingsley, R., Convergence of Probability Measures. John Wiley, New York, 1968.Google Scholar
2. Borodin, A. N., Limit Theorems for Sums of Independent Random Variables Defined on a Two Dimensional Random Walk. LOMI Preprints, 1980.Google Scholar
3. Kesten, H. and Spitzer, F., A Limit Theorem Related to a New Class of Self Similar Processes, Z. W. G. 50 (1979), 5–25.Google Scholar
4. Kipnis, C. and S. Varadhan, R. S., Central Limit Theorem for Additive Functionsals of Reversible Markov Processes and Applications to Simple Exclusions, Commun. Math. Phys. 104 (1986), 1–19.Google Scholar
5. Remillard, B. and Dawson, D. A., Laws of the Iterated Logarithm and Large Deviations for a Class of Diffusion Processes, Can. J. Statist. 17 (1989), 349–376.Google Scholar