Exponential Convergence in Probability for Empirical Means of Brownian Motion and of Random Walks期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Liming Wu

Affiliation:	(1) Laboratoire de Mathématiques Appliquées, CNRS-UMR 6620, Université, Blaise Pascal, 63177 Aubierre, France

Abstract:	Given a Brownian motion (B_t)_t0 in R^d and a measurable real function f on R^d belonging to the Kato class, we show that 1/t ₀^tf(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
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