Gaussian measures on Lp spaces, 1 ≤ p < ∞
نویسندگان
چکیده
منابع مشابه
On convex risk measures on Lp-spaces
Much of the recent literature on risk measures is concerned with essentially bounded risks in L∞. In this paper we investigate in detail continuity and representation properties of convex risk measures on L spaces. This frame for risks is natural from the point of view of applications since risks are typically modelled by unbounded random variables. The various continuity properties of risk mea...
متن کاملA NOTE ON THE SPACES Lp FOR 0 < p < 1
It is shown that there is no Hausdorff vector topology p on the space Lp (where 0 < p < 1) such that the unit ball of Lp is relatively compact for the topology p. It is well known that the space L1 (0, 1) is not a dual Banach space; this follows from the Krein-Milman theorem. It is not even isomorphic to a dual space, by a result due to Gelfand [2] (see Bessaga and Pelczyn'ski [1] and Namioka [...
متن کاملON THE LOWER TAIL OF GAUSSIAN MEASURES ON lp
where Cα,p and Dα,p are positive constants. This extends the results (Theorem 4.1-4.4) of Hoffmann-Jørgensen, Shepp and Dudley[4] for p = 2 and can be used to determine the nature rate of escape for an independent coordinate lp-valued Brownian motion for p > 2 (see Cox[2] and Erickson[3]). As a consequence of (1.2), we give a positive answer to a conjecture in Erickson[3]. In section 3, as an a...
متن کاملGaussian Measures as Limits on Irreducible Symmetric Spaces and Cones
We prove central limit theorems of Lindeberg-L evy and Lindeberg-Feller type for any K-invariant random variables on all irreducible symmetric spaces and irreducible symmetric cones, completing in this way the numerous partial results known before. In all cases the limit measures turn out to be Gaussian and being such a limit characterizes these measures. On the other hand we show that other cl...
متن کاملTotally probabilistic Lp spaces
In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.
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: Journal of Multivariate Analysis
سال: 1972
ISSN: 0047-259X
DOI: 10.1016/0047-259x(72)90034-6