Tagged Questions
0
votes
1answer
65 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 ...
2
votes
2answers
122 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
vote
1answer
66 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 ...
6
votes
0answers
187 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 ...
4
votes
2answers
233 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 ...
1
vote
0answers
57 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 ...
