References
- Markov processes characterization and convergence Ethier;T.Kurtz
- Convergence of stochastic processes. Spinger series in Statistics D.Pollard
- Stochastic integration and differential equations : A New Approach Protter
Journal of the Korean Statistical Society
- Volume 24 Issue 1
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- Pages.225-231
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- 1995
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- 1226-3192(pISSN)
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- 2005-2863(eISSN)
A Uniform CLT for Continuous Martingales
- Bae, Jong-Sig (Department of Mathematics, Sung Kyun Kwan University, Suwon 440-740) ;
- Shlomo Leventatl (Department of Statistics and Probability, Michigan State University, East Lansing, Michigan 48824)
- Published : 1995.06.01
Abstract
An eventual uniform equicontinuity condition is investigated in the context of the uniform central limit theorem (UCLT) for continuous martingales. We assume the usual intergrability condition on metric entropy. We establish an exponential inequality for a martingales. Then we use the chaining lemma of Pollard (1984) to prove an eventual uniform equicontinuity which is a sufficient condition of UCLT. We apply the result to approximate a stochastic integral with respect to a martingale to that of a Brownian motion.
Keywords
- Continuous martingales;
- Eventual uniform equicontinuity;
- Uniform central limit theorem;
- Chaining argument