Questions tagged [nonlinear-dynamical-system]
6 questions
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Chaos theory, equation-free modeling and non-parametric statistics
Being interested in complex systems and trying to get a beginner's understanding of the field, today I ran across this interesting article in Quanta Magazine on chaos theory and equation-free modeling. I realize that non-parametric statistics…
Aleksandr Blekh
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Do stochastic chaotic systems decorrelate with time?
Assume I have a dynamical system with additive process noise of the form
$$\mathbf{x}_{t} = \mathbf{F}\left(\mathbf{x_{t-1}}\right) + \mathbf{\epsilon}$$
where $\mathbf{x}_{t}$ is the state at time $t$ and $\mathbf{\epsilon}$ is some form of…
J.Galt
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Time Varying Coefficients vs Rolling Estimation
What are the practical differences for forecasting from fitting a model with time varying coefficients vs. estimating a model with fixed parameters over rolling windows? Intuitively it seems that these approaches both attempt to capture time…
mgilbert
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Kalman Filter and Monte Carlo
What is the consequence on the uncertainty of our estimate when applying the standard kalman filter to nonlinear systems?
If we are unaware of the functional form of these non linear systems how do we proceed? In an extended Kalman filter, do we not…
Kaykhusraw
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Meaning of a scaling constant in a well-calibrated model
I'm reading this paper on safe model-based reinforcement learning.
Assumption 2 in this paper states:
Let $\mu_n(\cdot)$ and $\Sigma_n(\cdot)$ denote the posterior mean and covariance matrix functions of the statistical model of the dynamics (1)…
alexanderd5398
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Is there an estimator for the existence of Lyapunov-motivated stability?
Preface: This question is now asking about dynamical stability in a particular sense, and whether its existence can be inferred from data. It is motivated by commentary below the question "Is there a statistical analogue of the quantum mechanical…
DifferentialPleiometry
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