Uniform Ergodicity of Lotz–Räbiger Nets of Markov Operators on Abstract State Spaces

2018 ◽  
Vol 73 (1) ◽  
Author(s):  
Nazife Erkurşun Özcan ◽  
Farrukh Mukhamedov
Keyword(s):  
State Spaces ◽  
Markov Operators ◽  
Uniform Ergodicity

scholarly journals SPECTRAL CONDITIONS FOR UNIFORM P-ERGODICITIES OF MARKOV OPERATORS ON ABSTRACT STATES SPACES

2020 ◽  
pp. 1-15
Author(s):  
NAZIFE ERKURŞUN-ÖZCAN ◽  
FARRUKH MUKHAMEDOV
Keyword(s):  
Banach Space ◽  
Rate Of Convergence ◽  
Spectral Radius ◽  
Markov Operator ◽  
Asymptotical Stability ◽  
Ordered Banach Space ◽  
State Spaces ◽  
Markov Operators ◽  
Positive Elements

Abstract In the present paper, we deal with asymptotical stability of Markov operators acting on abstract state spaces (i.e. an ordered Banach space, where the norm has an additivity property on the cone of positive elements). Basically, we are interested in the rate of convergence when a Markov operator T satisfies the uniform P-ergodicity, i.e. $\|T^n-P\|\to 0$ , here P is a projection. We have showed that T is uniformly P-ergodic if and only if $\|T^n-P\|\leq C\beta^n$ , $0<\beta<1$ . In this paper, we prove that such a β is characterized by the spectral radius of T − P. Moreover, we give Deoblin’s kind of conditions for the uniform P-ergodicity of Markov operators.

scholarly journals Dynamical system analysis of FLRW models with Modified Chaplygin gas

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Osman Yılmaz ◽  
Ertan Güdekli
Keyword(s):  
Dynamical System ◽  
Equation Of State ◽  
Energy Density ◽  
System Analysis ◽  
Chaplygin Gas ◽  
Modified Chaplygin Gas ◽  
State Spaces ◽  
The Universe ◽  
Matter Energy ◽  
Far Future

AbstractWe investigate Friedmann–Lamaitre–Robertson–Walker (FLRW) models with modified Chaplygin gas and cosmological constant, using dynamical system methods. We assume $$p=(\gamma -1)\mu -\dfrac{A}{\mu ^\alpha }$$ p = ( γ - 1 ) μ - A μ α as equation of state where $$\mu$$ μ is the matter-energy density, p is the pressure, $$\alpha$$ α is a parameter which can take on values $$0<\alpha \le 1$$ 0 < α ≤ 1 as well as A and $$\gamma$$ γ are positive constants. We draw the state spaces and analyze the nature of the singularity at the beginning, as well as the fate of the universe in the far future. In particular, we address the question whether there is a solution which is stable for all the cases.

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 Exact and fully symbolic verification of linear hybrid automata with large discrete state spaces

2012 ◽  
Vol 77 (10-11) ◽  
pp. 1122-1150 ◽  
Author(s):  
Werner Damm ◽  
Henning Dierks ◽  
Stefan Disch ◽  
Willem Hagemann ◽  
Florian Pigorsch ◽  
...  
Keyword(s):  
Hybrid Automata ◽  
State Spaces ◽  
Discrete State ◽  
Linear Hybrid Automata ◽  
Symbolic Verification

scholarly journals Local model checking for infinite state spaces

1992 ◽  
Vol 96 (1) ◽  
pp. 157-174 ◽  
Author(s):  
Julian Bradfield ◽  
Colin Stirling
Keyword(s):  
Model Checking ◽  
Local Model ◽  
State Spaces ◽  
Infinite State ◽  
Local Model Checking

Immune-Based Systems on Network Security Situation Awareness and Risk Prediction Model

2014 ◽  
Vol 643 ◽  
pp. 99-104
Author(s):  
Jin Yang ◽  
Yun Jie Li ◽  
Qin Li
Keyword(s):  
Situation Awareness ◽  
Artificial Immune Systems ◽  
Epidemic Spreading ◽  
State Spaces ◽  
Real Time Processing ◽  
Network Intrusion ◽  
Markov Chain Theory ◽  
Proposed Model ◽  
Network Risk

In this paper, the process of the developments and changes of the network intrusion behaviors were analyzed. An improved epidemic spreading model was proposed to study the mechanisms of aggressive behaviors spreading, to predict the future course of an outbreak and to evaluate strategies to control a network epidemic. Based on Artificial Immune Systems, the concepts and formal definitions of immune cells were given. And in this paper, the forecasting algorithm based on Markov chain theory was proposed to improve the precision of network risk forecasting. The data of the Memory cells were analyzed directly and kinds of state-spaces were formed, which can be used to predict the risk of network situation by analyzing the cells status and the classification of optimal state. Experimental results show that the proposed model has the features of real-time processing for network situation awareness.

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