1
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2answers
43 views

Memoryless processes and independence

this is a mere question of definition, that one surely can figure out by conventional means, but maybe someone can just quickly give me the definition. What is a memoryless process? Following the ...
3
votes
2answers
73 views

Properties of matrix exponential

I know that the solution to system $x' = Ax$ is $e^{At}$, and I'm aware of various methods to calculate the exponential numerically. However I wonder if there are some analytical results. Namely, I'm ...
0
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0answers
27 views

Invariant measure for a random dynamical system

I want to construct a random dynamical system over a metric space. To construct the metric space I require that the transformation be measure preserving. If I want my random mappings to be chosen ...
1
vote
1answer
110 views

Random Dynamical Systems: Intuitive Understanding

I am having trouble understanding this definition, [Arnold: Random Dynamical Systems]: Definition: A measurable random dynamical system on the measurable space $(X,\mathcal{B})$ over a metric ...
0
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1answer
763 views

Continuous-time versus discrete-time stochastic models

When modeling a dynamic phenomenon, (from a general point of view) people can use two type of models: (1) continuous-time models, (2) discrete-time models. To be more precise, assume that we try to ...
3
votes
2answers
280 views

How can a Markov chain be written as a measure-preserving dynamic system

From http://masi.cscs.lsa.umich.edu/~crshalizi/notabene/ergodic-theory.html irreducible Markov chains with finite state spaces are ergodic processes, since they have a unique invariant ...
1
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1answer
70 views

Parametric uncertainty in conditional term of piecewise nonlinear dynamical system

Consider a Hammerstein nonlinear dynamical system of the form $\mathbf{\dot{x}} = \mathbf{Ax} + \mathbf{Bu}$, where the non-linearity is in the control term $\mathbf{u}$, and has a piecewise ...
10
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1answer
348 views

Is a Markov process a random dynamic system?

A random dynamic system is defined in Wikipedia. Its definition, which is not included in this post for the sake of clarity, reminds me how similar a Markov process is to a random dynamic system just ...
5
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2answers
371 views

Example of a process that is ergodic but not mixing?

I recently heard a talk which depended on the dynamics of a system being mixing. I was told, and Wikipedia confirms, that "mixing" is a stronger condition than "ergodic", but after comparing the ...
2
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1answer
105 views

Examples when Resonance Overlap fails to predict the onset of Chaos

In a Hamiltonian system Chirikov's resonance overlap criterion approximately predicts the onset of chaotic behavior. Furthermore in a system where resonances overlap, the strengths of the resonances ...