The First Order Asymptotics of Waiting Times between Stationary Processes under Nonstandard Conditions
نویسنده
چکیده
We give necessary and sufficient conditions for the almost sure convergence of − 1 n logQ(B(X 1 ,D)) when (Xn)n≥1 is stationary and ergodic and when Q is stationary and satisfies certain strong mixing conditions. B(x1 ,D) is the single letter, additive distortion ball of radius D at the point x1 := (x1, . . . , xn). The asymptotic behavior of this quantity arises frequently in rate distortion theory, particularly when looking at the asymptotics of waiting times until a match (allowing distortion) between two stationary processes.
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To myself and my parents... iii ACKNOWLEDGEMENTS Throughout my graduate studies, I am indebted to many people for their help and encouragement. First of all, I would like to thank my advisor Prof. Hayriye Ayhan. It is impossible for me to express in words my full appreciation. However, I would like to thank all of her advice and support during my graduate studies. I would not have completed thi...
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