Asymptotic Behavior of Small Ball Probabilities M.A. Lifshits
The typical problem of the small ball probabilities is to investigate the asymptotic behavior of P {||X|| < r}, r → 0, for a random vector X taking values in a normed space. As a generic example, take a sample path of a random function as X and consider P {sup |Xt | < r}, r → 0. t∈T
The subject is known for long time to be hard but there was substantial progress during last years. We survey the recent results with special focus on the fruitful connection between Gaussian small ball probabilities and analytical problems of approximation theory.
Asymptotic Behavior of Small Ball Probabilities MA ...
The typical problem of the small ball probabilities is to investigate the asymptotic behavior of P{||X|| < r}, r â 0, for a random vector X taking values in a normed space. As a generic example, take a sample path of a ran- dom function as X and consider. P{sup tâT. |Xt| < r}, r â 0. The subject is known for long time to be hard ...
We obtain evaluations of probabilities of shifted small balls for the centered. Poisson process by making use of a density argument which, for the Poisson process, plays a role similar to that of the Cameron-Martin formula for the. Wiener process. 1.
Page 1. Probabilities of Randomly Centered Small Balls and. Quantization in Banach Space. S.Dereich and M.A. Lifshits. We investigate the Gaussian small ball probabilities with ran- dom centers, find their deterministic a.s.-equivalents and establish
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Robust Maximization of Asymptotic Growth under Covariance Uncertainty. Erhan Bayraktar and Yu-Jui Huang. Department of Mathematics, University of Michigan. The Question. How to maximize the growth rate of one's wealth when precise covariance structur
Oct 1, 2012 - Abstract. We characterize the asymptotic independence between blocks consisting of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth moment theorem of Nualart and Peccati, its mul
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IV Statistics with Many Instruments. 113. Lemma 6 of Phillips and Moon (1999) provides general conditions under which sequential convergence implies joint convergence. Phillips and Moon (1999), Lemma 6. (a) Suppose there exist random vectors XK and X
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