A strong law of large numbers for martingale arrays
نویسنده
چکیده
Abstract: We prove a martingale triangular array generalization of the Chow-BirnbaumMarshall’s inequality. The result is used to derive a strong law of large numbers for martingale triangular arrays whose rows are asymptotically stable in a certain sense. To illustrate, we derive a simple proof, based on martingale arguments, of the consistency of kernel regression with dependent data. Another application can be found in [1] where the new inequality is used to prove a strong law of large numbers for adaptive Markov Chain Monte Carlo methods. AMS 2000 subject classifications: Primary 60J27, 60J35, 65C40.
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