scholarly journals Higher moments of Banach space valued random variables

2015 ◽  
Vol 238 (1127) ◽  
pp. 0-0 ◽  
Author(s):  
Svante Janson ◽  
Sten Kaijser
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Higher Moments

scholarly journals The space $D$ in several variables: random variables and higher moments

2021 ◽  
Vol 127 (3) ◽  
Author(s):  
Svante Janson
Keyword(s):  
Banach Space ◽  
Dual Space ◽  
Random Variables ◽  
Higher Moments ◽  
Multilinear Form ◽  
Standard Case ◽  
Random Functions ◽  
Several Variables ◽  
Random Elements ◽  
Point Evaluations

We study the Banach space $D([0,1]^m)$ of functions of several variables that are (in a certain sense) right-continuous with left limits, and extend several results previously known for the standard case $m=1$. We give, for example, a description of the dual space, and we show that a bounded multilinear form always is measurable with respect to the $\sigma$-field generated by the point evaluations. These results are used to study random functions in the space. (I.e., random elements of the space.) In particular, we give results on existence of moments (in different senses) of such random functions, and we give an application to the Zolotarev distance between two such random functions.

scholarly journals Some results on the span of families of Banach valued independent, random variables

1991 ◽  
Vol 14 (2) ◽  
pp. 381-384
Author(s):  
Rohan Hemasinha
Keyword(s):  
Banach Space ◽  
Probability Space ◽  
Linear Span ◽  
Random Variables ◽  
Isomorphic Copy ◽  
Independent Random Variables ◽  
Closed Linear Span

LetEbe a Banach space, and let(Ω,ℱ,P)be a probability space. IfL1(Ω)contains an isomorphic copy ofL1[0,1]then inLEP(Ω)(1≤P<∞), the closed linear span of every sequence of independent,Evalued mean zero random variables has infinite codimension. IfEis reflexive orB-convex and1<P<∞then the closed(in LEP(Ω))linear span of any family of independent,Evalued, mean zero random variables is super-reflexive.

scholarly journals On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 727 ◽  
Author(s):  
Dongming Nie ◽  
Saima Rashid ◽  
Ahmet Ocak Akdemir ◽  
Dumitru Baleanu ◽  
Jia-Bao Liu
Keyword(s):  
Numerical Analysis ◽  
Integral Inequality ◽  
Convex Functions ◽  
Random Variables ◽  
Higher Moments ◽  
Weighted Inequalities ◽  
Convex Mapping ◽  
Error Estimations ◽  
Moments Of Random Variables

In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

scholarly journals The divergence of Banach space valued random variables on Wiener space

2007 ◽  
Vol 140 (3-4) ◽  
pp. 631-633 ◽  
Author(s):  
E. Mayer-Wolf ◽  
M. Zakai
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Wiener Space
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