Exponential Convergence in Probability for Empirical Means of Brownian Motion and of Random Walks

Liming Wu ()
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Liming Wu: Université

Journal of Theoretical Probability, 1999, vol. 12, issue 3, 661-673

Abstract: Abstract Given a Brownian motion (B t) t≥0 in R d and a measurable real function f on R d belonging to the Kato class, we show that 1/t ∫ 0 t f(B s ) ds converges to a constant z with an exponential rate in probability if and only if f has a uniform mean z. A similar result is also established in the case of random walks.

Keywords: Exponential convergence in probability; large deviations; Brownian motion; random walks (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1023/A:1021671630755

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