scholarly journals Stability of the Markov operator and synchronization of Markovian random products

Nonlinearity ◽  
2018 ◽  
Vol 31 (5) ◽  
pp. 1782-1806 ◽  
Author(s):  
Lorenzo J Díaz ◽  
Edgar Matias
Keyword(s):  
Markov Operator ◽  
Random Products

Factorization of an adjontable Markov operator

2019 ◽  
Vol 22 (02) ◽  
pp. 1950013
Author(s):  
Carlo Pandiscia
Keyword(s):  
Hilbert Space ◽  
Matrix Algebra ◽  
Unitary Operator ◽  
Markov Operator ◽  
Factorization Property ◽  
Markov Operators ◽  
Dilation Theory ◽  
Probability Spaces

In this work, we propose a method to investigate the factorization property of a adjontable Markov operator between two algebraic probability spaces without using the dilation theory. Assuming the existence of an anti-unitary operator on Hilbert space related to Stinespring representations of our Markov operator, which satisfy some particular modular relations, we prove that it admits a factorization. The method is tested on the two typologies of maps which we know admits a factorization, the Markov operators between commutative probability spaces and adjontable homomorphism. Subsequently, we apply these methods to particular adjontable Markov operator between matrix algebra which fixes the diagonal.

scholarly journals Asymptotics for self-normalized random products of sums of i.i.d. random variables

2007 ◽  
Vol 334 (2) ◽  
pp. 1246-1259 ◽  
Author(s):  
Tian-Xiao Pang ◽  
Zheng-Yan Lin ◽  
Kyo-Shin Hwang
Keyword(s):  
Random Variables ◽  
Products Of Sums ◽  
Random Products

scholarly journals Noncommuting random products

1963 ◽  
Vol 108 (3) ◽  
pp. 377-377 ◽  
Author(s):  
Harry Furstenberg
Keyword(s):  
Random Products

scholarly journals Tails of Stopped Random Products: The Factoid and Some Relatives

2008 ◽  
Vol 45 (04) ◽  
pp. 1161-1180
Author(s):  
Anthony G. Pakes
Keyword(s):  
Tail Behaviour ◽  
Random Product ◽  
Random Products ◽  
Heavy Tailed ◽  
First Time ◽  
Independent And Identically Distributed

The upper tail behaviour is explored for a stopped random product ∏j=1NXj, where the factors are positive and independent and identically distributed, andNis the first time one of the factors occupies a subset of the positive reals. This structure is motivated by a heavy-tailed analogue of the factorialn!, called the factoid ofn. Properties of the factoid suggested by computer explorations are shown to be valid. Two topics about the determination of the Zipf exponent in the rank-size law for city sizes are discussed.

scholarly journals A Limit Theorem for Random Products of Trimmed Sums of i.i.d. Random Variables

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Fa-mei Zheng
Keyword(s):  
Distribution Function ◽  
Limit Theorem ◽  
Wiener Process ◽  
Continuous Distribution ◽  
Random Variables ◽  
Standard Wiener Process ◽  
Trimmed Sums ◽  
Fixed Constant ◽  
Random Products ◽  
Trimmed Sum

Let be a sequence of independent and identically distributed positive random variables with a continuous distribution function , and has a medium tail. Denote and , where , , and is a fixed constant. Under some suitable conditions, we show that , as , where is the trimmed sum and is a standard Wiener process.

scholarly journals The spectrum of an Adelic Markov operator

2015 ◽  
Vol 64 (5) ◽  
pp. 1465-1512
Author(s):  
Andreas Knauf
Keyword(s):  
Markov Operator

scholarly journals Weak Markov operators

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5453-5457
Author(s):  
Hūlya Duru ◽  
Serkan Ilter
Keyword(s):  
Positive Operator ◽  
Extreme Points ◽  
Markov Operator ◽  
Weak Order ◽  
Markov Operators

Let A and B be f -algebras with unit elements eA and eB respectively. A positive operator T from A to B satisfying T(eA) = eB is called a Markov operator. In this definition we replace unit elements with weak order units and, in this case, call T to be a weak Markov operator. In this paper, we characterize extreme points of the weak Markov operators.

Markov operator in constrained tomography

1992 ◽  
Author(s):  
P. Carrion ◽  
G. Jacovitti ◽  
A. Neri
Keyword(s):  
Markov Operator
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