scholarly journals A $q$-Analogue of de Finetti's Theorem

10.37236/167 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Alexander Gnedin ◽  
Grigori Olshanski
Keyword(s):  
Boundary Problem ◽  
Galois Field ◽  
Infinite Group ◽  
Natural Action ◽  
De Finetti’S Theorem ◽  
De Finetti's Theorem ◽  
Invertible Matrices

A $q$-analogue of de Finetti's theorem is obtained in terms of a boundary problem for the $q$-Pascal graph. For $q$ a power of prime this leads to a characterisation of random spaces over the Galois field ${\Bbb F}_q$ that are invariant under the natural action of the infinite group of invertible matrices with coefficients from ${\Bbb F}_q$.

A normal form theorem for Lω1p, with applications

1982 ◽  
Vol 47 (3) ◽  
pp. 605-624 ◽  
Author(s):  
Douglas N. Hoover
Keyword(s):  
Normal Form ◽  
Probability Model ◽  
Random Variables ◽  
Interpolation Theorem ◽  
Complete Theory ◽  
De Finetti’S Theorem ◽  
Form Theorem ◽  
Normal Form Theorem ◽  
De Finetti's Theorem

AbstractWe show that every formula of Lω1P is equivalent to one which is a propositional combination of formulas with only one quantifier. It follows that the complete theory of a probability model is determined by the distribution of a family of random variables induced by the model. We characterize the class of distribution which can arise in such a way. We use these results together with a form of de Finetti’s theorem to prove an almost sure interpolation theorem for Lω1P.

scholarly journals De Finetti’s Theorem in Categorical Probability

2021 ◽  
Vol 2 (4) ◽  
Author(s):  
Tobias Fritz ◽  
Tomáš Gonda ◽  
Paolo Perrone
Keyword(s):  
De Finetti’S Theorem ◽  
De Finetti's Theorem

A class of non-identifiable stochastic models

1977 ◽  
Vol 14 (3) ◽  
pp. 475-482 ◽  
Author(s):  
Violet R. Cane
Keyword(s):  
Stochastic Process ◽  
Poisson Process ◽  
Stochastic Models ◽  
Birth Process ◽  
De Finetti’S Theorem ◽  
Polya Process ◽  
To Come ◽  
Pólya Process ◽  
De Finetti's Theorem ◽  
Random Times

If events occur in time according to a stochastic process then, under not very restrictive conditions, each realization will appear to come from a Poisson process with its own rate provided that the events in the realization occur at effectively random times. This result is related to de Finetti's theorem on exchangeable events. Particular applications are to the Pólya process describing accidents and the pure birth process.

scholarly journals FRACTAL CLUSTERING OF GROUP CODES IN THE SYSTEM OF GALOIS FIELD

2020 ◽  
Vol 62 (4) ◽  
pp. 85-92
Author(s):  
Anatolii A. Gladkikh ◽  
◽  
Anastasiia D. Bakurova ◽  
Artem V. Menovshchikov ◽  
Basem A.S. Said ◽  
...  
Keyword(s):  
Integrated Circuits ◽  
Computational Procedure ◽  
Block Code ◽  
Galois Field ◽  
Digital Data ◽  
New Combination ◽  
Redundant Data ◽  
Memory Card ◽  
Generating Matrix ◽  
Invertible Matrices

The permutation decoding (PD) of group systematic noise-immune codes is proved to be the most efficient method in using the redundant data entered to the code as against other methods of decoding digital data [1-5]. This opens up the opportunity of solving a complex computational problem of finding an equivalent code (EC), which is used to search for the error vector. The essence of this solution is that the computational procedure of real-time search for EC for each new combination of redundant code is replaced by a preliminary process of training the decoder to put in accordance with each new permutation of characters the generating matrix of EC parameters, which are recorded in the decoder’s memory card during training. Thus, such a memory card is called a cognitive card (CC). The article estimates the memory size of the CC, when using the block code (15,7,5), and shows the possibility of implementing a permutation decoder on basis of existing integrated circuits based on proven statements. For the first time, the apparatus of fractal partitioning of augmented binary Galois fields using the clustering of the common space of code vectors of a given code is used to prove the main statements. An efficient algorithm is presented to search for a set of invertible matrices of rearranged codes that do not provide an EC and for this reason should be primarily detected in the decoding procedure of the received code vectors.

De Finetti's Theorem on Exchangeable Variables

1976 ◽  
Vol 30 (4) ◽  
pp. 188 ◽  
Author(s):  
David Heath ◽  
William Sudderth
Keyword(s):  
De Finetti’S Theorem ◽  
De Finetti's Theorem
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