However, both these cases consider the ability
of stochastic variation to drive the formation of a single stable attractor.
That requires a model
of the stochastic variations in the data and a precise definition of, what the trend means in the particular consideration.
Not exact matches
Time
variation of the
stochastic discount tells us to expect low returns on equity during good economic times.
«
Stochastic variations of migration speed between cells in clonal populations.»
It amazes me that so much
of the natural
variation we observe within and across species is due simply to
stochastic processes in the population.
We found much higher variance in RND values for intronic fragments consisting
of a reduced number
of sites, likely due to
stochastic variation in the mutation process.
None
of the random permutations exceeded the observed differentiation (P < 0.001), indicating that these regions
of differentiation are unlikely to reflect simple
stochastic variation in differentiation across the genome due to the reduced number
of individuals sampled.
It produces a much more detailed view
of the state
of nuclear DNA inside a cell population, showing the enormous
variations in
stochastic mutational damage that takes place over the years.
Broadly speaking, however, analysis
of transcriptional regulation at the single cell level has provided evidence for a strong
stochastic element: genetically identical cells within the same environment show significant
variation in molecular phenotype, in a fluctuating manner [24].
tpinlb, climate models don't «predict» year - specific phenomena arising from
stochastic variation that adds «noise» to progression
of climate states under the influence
of persistent forcings.
However,
stochastic weather
variations will lead to differing amounts
of cooling for synoptically distinct regions.
• There is strong evidence that the multidecadal SAT variability in the Atlantic (and globally) is driven (at least partly) by
variations in the MOC • A
stochastic scenario is most plausible, in which the ocean is driven by the low - frequency portion
of the atmospheric variability (NAO).
I propose the following Climatic null hypothesis that: «Natural climatic
variation is quantified by the
stochastic uncertainty envelope
of historical and paleo data, embodying the nonlinear chaotic interaction
of atmospheric, oceanic, volcanic, solar, and galactic processes, including climate persistence quantified by Hurst - Kolmogorov dynamics.»
«Natural climatic
variation is quantified by the
stochastic uncertainty envelope
of historical and paleo data, embodying the nonlinear chaotic interaction
of atmospheric, oceanic, volcanic, solar, and galactic processes, including climate persistence quantified by Hurst - Kolmogorov dynamics.»
We investigate three methods for simultaneous estimation
of the Hurst parameter (H) and the standard deviation (σ) for a Hurst - Kolmogorov
stochastic process, namely the maximum likelihood method and two methods based on the
variation of the standard deviation or
of the variance with time scale.
Nevertheless, the salutary aspect
of the GISP 2 data is the clear indication it provides
of a gentle, truly secular cooling trend since the Holocene optimum, overlain by weakly stationary, strongly structured, quasi-Gaussian
stochastic variations whose ordinate distribution and power - spectrum both diverge from anything resembling a Poisson process
of abrupt jumps.
Although it is clear that further attention is required in defining and characterizing the aspects
of this
variation (e.g. frequency and amplitude [44,65]-RRB- that lead to differences in species responses, a more immediate empirical challenge is to characterize and separate the effects
of periodic,
stochastic and / or cyclical natural
variations [61] from directional change imposed by long - term climatic forcing.
But once you look at the rate
of change you start to realise that it's not just random noise or «
stochastic»
variation.
There's a
stochastic component to «energy in» due to
variation in solar output, wobble, orbital asymmetry, albedo and a whole host
of other factors (even small things like kinetic energy that is transferred from meteorites and space dust that is constantly hitting the earth).