scholarly journals Strong Law of Large Numbers of Pettis-Integrable Multifunctions

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Hamid Oulghazi ◽  
Fatima Ezzaki
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Mosco Convergence ◽  
Weakly Compact ◽  
Strong Law ◽  
Large Numbers ◽  
Reversed Martingale ◽  
Integrable Martingale

Using reversed martingale techniques, we prove the strong law of large numbres for independent Pettis-integrable multifunctions with convex weakly compact values in a Banach space. The Mosco convergence of reversed Pettis-integrable martingale of the form (EBnX)n≥1, where (Bn)n≥1 is a decreasing sequence of the sub σ-algebra of F is provided.

Sample Behavior and Laws of Large Numbers for Gaussian Random Elements

2003 ◽  
Vol 10 (4) ◽  
pp. 637-676
Author(s):  
Z. Ergemlidze ◽  
A. Shangua ◽  
V. Tarieladze
Keyword(s):  
Banach Space ◽  
Law Of Large Numbers ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

Abstract Criteria for almost sure boundedness and convergence to zero almost surely of Banach space valued independent Gaussian random elements are found. The obtained statements can be viewed as vector-valued versions of the corresponding results due to N. Vakhania. Moreover, from the obtained statements a strong law of large numbers is derived in the form of Yu. V. Prokhorov.

scholarly journals Strong Laws of Large Numbers for𝔹-Valued Random Fields

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Zbigniew A. Lagodowski
Keyword(s):  
Banach Space ◽  
Random Fields ◽  
Law Of Large Numbers ◽  
Random Vectors ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Geometry Of Banach Space ◽  
Necessary And Sufficient

We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) for𝔹-valued random vectors under geometric assumptions. Also, we give probabilistic requirements for above-mentioned SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic conditions for the geometry of Banach space associated to the strong and weak law of large numbers for multidimensionally indexed random vectors.

scholarly journals Limit theorems for fuzzy random variables

1986 ◽  
Vol 407 (1832) ◽  
pp. 171-182 ◽  
Keyword(s):  
Banach Space ◽  
Limit Theorem ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Embedding Theorems ◽  
Fuzzy Random Variables ◽  
Strong Law ◽  
Large Numbers ◽  
Fuzzy Random

A strong law of large numbers and a central limit theorem are proved for independent and identically distributed fuzzy random variables, whose values are fuzzy sets with compact levels. The proofs are based on embedding theorems as well as on probability techniques in Banach space.

Sign in / Sign up

Export Citation Format

Share Document