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Random Dynamical Systems

2016
In this chapter we will introduce methods and techniques to analyze models with stochasticity or randomness. In particular we will establish the framework of random dynamical systems and introduce the concept of random attractors.
Tomás Caraballo, Xiaoying Han
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Random Dynamical Systems

2007
This treatment provides an exposition of discrete time dynamic processes evolving over an infinite horizon. Chapter 1 reviews some mathematical results from the theory of deterministic dynamical systems, with particular emphasis on applications to economics. The theory of irreducible Markov processes, especially Markov chains, is surveyed in Chapter 2.
Rabi Bhattacharya, Mukul Majumdar
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Wigner distribution for random systems

Journal of Modern Optics, 2002
We use the Wigner distribution to study systems subjected to random forces. We define the instantaneous spectrum as the ensemble average of the Wigner distribution, and we write the differential equation whose solution gives us the time-varying spectrum of the state variable. We consider the cases of both constant and time-varying coefficients.
GALLEANI, Lorenzo, COHEN L.
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Partial realization of random systems

Automatica, 1972
Abstract An algorithm is presented for the recursive determination of certain lumped linear models that when driven by a white-noise sequence yield outputs whose covariances match increasing sections of a given covariance sequence.
Rissanen, J., Kailath, T.
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Random Independence Systems

1981
Abstract : This report introduces a new random structure generalizing matroids. These random independence systems allow us to develop general techniques for solving hard combinatorial optimization problems with random inputs.
Paul G. Spirakis, John H. Reif
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Random Hyperbolic Systems

2007
We review definitions of random hyperbolic sets and introduce a characterization using random cones. Moreover we discuss problems connected with symbolic representations and the thermodynamic formalism for random hyperbolic systems both in discrete and continuous time cases.
Volker Matthias Gundlach, Yuri Kifer
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Random dynamical systems

1995
This paper was given as a presentation at the Jahrestagung der DMV in Berlin, 1992. It provides an overview of the theory of random dynamical systems (RDS's), and covers in a very short, but precise way the state of the art in the following areas: 1. Metric, topological, and smooth dynamics, 2. RDS: concept, invariant measures, 3. Generation of RDS, 4.
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Quantum Random Systems

1998
In Chap. 3, we discussed the statistical properties of an N-particle system treated within the framework of classical mechanics. In this chapter, we will take the more fundamental point of view that the particles and their interactions have to be described quantum mechanically. In quantum mechanics, the state of a system has to be described by a vector
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Random Parallel Systems

2014
High system reliability can be achieved by redundancy and maintenance. The most typical model is a standard parallel system which consists of \(n\) identical units in parallel. It was originally shown that the system can operate for a specified mean time by either changing the replacement time or increasing the number of units [1, p. 65].
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Random field systems

Ferroelectrics, 1990
Abstract Spin models in weak random fields are good representations of a large number of impure compounds which undergo magnetic or structural transitions. From a theoretical point of view these systems exhibit frustration on a mesoscopic scale and take therefore an indermediate position between (spin) glasses and unfrustrated (diluted) disordered ...
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