Approximation of vector-valued random variables by constants
نویسندگان
چکیده
منابع مشابه
ASYMPTOTIC BEHAVIOR OF p-PREDICTIONS FOR VECTOR VALUED RANDOM VARIABLES
Let (Q,<r, p) be a probability space and let X be a B-valued /i-essentially bounded random variable, where (B,\\ ||) is a uniformly convex Banach space. Given a, a sub-<r-algebra of a, the p-prediction (1 < p < oo) of X is defined as the best Lp-approximation to X by (»-measurable random variables. The paper proves that the Pólya algorithm is successful, i.e. the p-prediction converges to an "c...
متن کاملGeneral Inner Approximation of Vector-valued Functions
This paper addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal. This paper extends this result to vector-valued functions with domain and co-domain of different dimensi...
متن کاملOn a quaternion valued Gaussian random variables
In the present note we show that Polya’s type characterization theorem of Gaussian distributions does not hold. This happens because in the linear form, constituted by the independent copies of quaternion random variables, a part of the quaternion coefficients is written on the right hand side and another part on the left side. This gives a negative answer to the question posed in [1]. Mathemat...
متن کاملApproximation for Expectations of Unbounded Functions of Dependent Integer-valued Random Variables
Expectations of unbounded functions of dependent nonnegative integer-valued random variables are approximated by the expectations of the functions of independent copies of these random variables. The Lindeberg method is used.
متن کاملProposition-valued random variables as information
The notion of a proposition as a set of possible worlds or states occupies central stage in probability theory, semantics and epistemology, where it serves as the fundamental unit both of information and meaning. But this fact should not blind us to the existence of prospects with a di¤erent structure. In the paper I examine the use of random variables in particular, proposition-valued random v...
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 Approximation Theory
سال: 1983
ISSN: 0021-9045
DOI: 10.1016/0021-9045(83)90061-8