Isoperimetry and Integrability of the Sum of Independent Banach-Space Valued Random Variables
نویسندگان
چکیده
منابع مشابه
Higher Moments of Banach Space Valued Random Variables
We define the k:th moment of a Banach space valued random variable as the expectation of its k:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals...
متن کاملModerate Deviation Principles for Trajectories of Sums of Independent Banach Space Valued Random Variables
Let {Xn} be a sequence of i.i.d. random vectors with values in a separable Banach space. Moderate deviation principles for trajectories of sums of {Xn} are proved, which generalize related results of Borovkov and Mogulskii (1980) and Deshayes and Picard (1979). As an application, functional laws of the iterated logarithm are given. The paper also contains concluding remarks, with examples, on e...
متن کاملCentral Limit Theorem for Banach Space Valued Fuzzy Random Variables
In this paper we prove a central limit theorem for Borel measurable nonseparably valued random elements in the case of Banach space valued fuzzy random variables.
متن کاملAsymptotic Expansions for the Laplace Approximations of Sums of Banach Space-valued Random Variables
Let Xi, i ∈ N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let Φ be a smooth enough mapping from B intoR. An asymptotic evaluation of Zn = E(exp(nΦ( ∑n i=1 Xi/n))), up to a factor (1 + o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305–318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221–238]. In this paper, a...
متن کاملOn the Banach-Space-Valued Azuma Inequality and Small-Set Isoperimetry of Alon-Roichman Graphs
We discuss the connection between the expansion of small sets in graphs, and the Schatten norms of their adjacency matrices. In conjunction with a variant of the Azuma inequality for uniformly smooth normed spaces, we deduce improved bounds on the small-set isoperimetry of Abelian Alon–Roichman random Cayley graphs.
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: The Annals of Probability
سال: 1989
ISSN: 0091-1798
DOI: 10.1214/aop/1176991174