منابع مشابه
A large-deviation inequality for vector-valued martingales
Let X = (X0, . . . , Xn) be a discrete-time martingale taking values in any real Euclidean space such that X0 = 0 and for all n, ‖Xn − Xn−1‖ ≤ 1. We prove the large deviation bound Pr [‖Xn‖ ≥ a] < 2e1−(a−1) 2/2n. This upper bound is within a constant factor, e2, of the AzumaHoeffding Inequality for real-valued martingales. This improves an earlier result of O. Kallenberg and R. Sztencel (1992)....
متن کاملOn Vector-valued Hardy Martingales and a Generalized Jensen’s Inequality
We establish a generalized Jensen’s inequality for analytic vector-valued functions on TN using a monotonicity property of vector-valued Hardy martingales. We then discuss how this result extends to functions on a compact abelian group G, which are analytic with respect to an order on the dual group. We also give a generalization of Helson and Lowdenslager’s version of Jensen’s inequality to ce...
متن کاملAdaptive vector-valued martingales: applications to image compression
Given a finite collection of functions defined on a common domain, the paper describes an algorithm that constructs a vector valued approximating martingale sequence. The orthonomal basis functions used to construct the martingale approximation are optimally selected, in each greedy step, from a large dictionary. The resulting approximations are characterized as generalized Hsystems and provide...
متن کاملVector–valued Walsh–Paley martingales and geometry of Banach spaces
Abstract The concept of Rademacher type p (1 ≤ p ≤ 2) plays an important role in the local theory of Banach spaces. In [3] Mascioni considers a weakening of this concept and shows that for a Banach space X weak Rademacher type p implies Rademacher type r for all r < p. As with Rademacher type p and weak Rademacher type p, we introduce the concept of Haar type p and weak Haar type p by replacing...
متن کاملConnecting Yule Process, Bisection and Binary Search Tree via Martingales
We present new links between some remarkable martingales found in the study of the Binary Search Tree or of the bisection problem, looking at them on the probability space of a continuous time binary branching process.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2013
ISSN: 0035-7596
DOI: 10.1216/rmj-2013-43-5-1553