Such Hurst phenomena have been observed
in the stochastic processes of nature in the area of hydrology (Hurst) and also in the proxy record of annual mean surface temperature at a millennial time scale (Barnett).
Personally I take little comfort in this, in part because my doctoral dissertation many decades ago concerned fluctuations in a threshold system (in nerve cells, but the principle applies elsewhere;
in stochastic processes, it goes under the name of the «first passage time problem»).
Not exact matches
Human life and Earth are simply a minute part of this chaotic,
stochastic, expanding, shrinking
process disappearing
in five billion years with the burn out of the Sun and maybe returning
in another five billion years with different life forms but still subject to the v - agaries of its local star.
Human life and Earth are simply a minute part of this chaotic,
stochastic, expanding, shrinking
process disappearing
in five billion years with the burn out of the Sun and maybe returning
in another five billion years with different life forms but still subject to the va - garies of its local star.
The choice between these possible futures is made,
in a condition of chemical instability, by
stochastic (nondeterministic)
processes, such as random internal fluctuations of the system.
Stochastic processes play an important role
in this theory.
The
stochastic spatial
processes interfere with the classic ecological theory of predictable dependence, resulting
in de facto independence.
In 2012, Vedral, Gu and others proved a similar result for another class of problems known as
stochastic processes.
These scientists and research groups have complementary expertise
in numerical analysis, computational science, dynamical systems, statistics, and
stochastic processes.
The first group participates
in an intensive 4 - week collaborative learning experience on dynamical systems (broadly understood to include
stochastic processes), modeling, and computational methods.
The main objective is to cover the field of financial mathematics
in a reasonably broad yet rigorous way, not just encompassing the replication of contingent claims
in a complete market setting, but also materials drawn from financial markets, financial theory, economics, econometrics, and
stochastic processes, together with related mathematical and computational techniques.
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.
Changes
in gene expression as a response to death, and during subsequent post-mortem ischemia, might be expected to reflect
stochastic variation resulting from the enzymatic
processes underlying mRNA degradation.
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.
Paper: Efficient analysis of
stochastic gene dynamics
in the non-adiabatic regime using piecewise deterministic Markov
processes, Yen Ting Lin and Nicolas E. Buchler, Royal Society Interface volume and date
Quantitative RNA ‐ FISH experiments
in combination with a
stochastic model of transcription reveal that antisense transcription disrupts the activity of the Set3 lysine deacetylase, thus altering the rates of sense transcript production,
processing and stability.
The next El Niño event (whenever it comes — that is a
stochastic process) is likely to produce a new global mean temperature record (as happened
in 2010).
As Richard Alley has shown
in a couple of papers, the ice core data of DO events are entirely consistent with
stochastic resonance — which is not chaos but arises from a simple threshold
process («flicking of a switch»)
in the presence of noise.
On these premises it is possible to shape a consistent
stochastic representation of natural
processes,
in which predictability (suggested by deterministic laws) and unpredictability (randomness) coexist and are not separable or additive components.
The climate scientists that worry about these issues don't post here (much - Jeff made a single post) so you aren't really going to see a meaningful discussion on the role of chaos or
stochastic processes on climates, how that is handled
in model building, and what that means
in terms of model verification.
In contrast, the research contributions of the hydrological community have been based on more pragmatic statistical and stochastic descriptions of natural processes, which reflect a different paradigm in both understanding and modelling natural processes..
In contrast, the research contributions of the hydrological community have been based on more pragmatic statistical and
stochastic descriptions of natural
processes, which reflect a different paradigm
in both understanding and modelling natural processes..
in both understanding and modelling natural
processes....
In fact, it's my experience modeling
stochastic processes and noise (which are inherently chaotic systems that can not be directly modeled except as probability functions) that informs this next statement: climate models can, and do, model cloud formation.
Physical
processes that involve turbulence or other deterministic chaos DO produce time - histories that are
stochastic in their variability.
Cross-spectral coherence has little to do with when extreme values are achieved
in a wide - band
stochastic process such as ENSO.
This approach is particularly appropriate given recent interest
in stochastic parametrization of subgrid - scale
processes in GCMs.
On the other hand, along with these,
stochastic nonstationary phenomena such as mixing, localization, and clustering
in the phase and the physical spaces can occur
in particular realizations of random
processes and fields.
«
In mathematics, the Ornstein — Uhlenbeck
process (named after Leonard Ornstein and George Eugene Uhlenbeck), is a
stochastic process that, roughly speaking, describes the velocity of a massive Brownian particle under the influence of friction.
Thirty years later, the relevance of this study has been realized
in the development of
stochastic approaches to represent cumulus convection and its upscale energy transports, and
in the emerging efforts to resolve these multi-scale
processes in atmospheric simulations at the cloud system - resolving scale (approx. 1 km).
I'm really more interested
in time series issues — there are lots of
stochastic processes for which there is no second moment, Mandelbrot identifies lots of them.
If we continue this type of thinking (means varying at a cascade of time scales,
in an unpredictable manner), the eventual result is a stationary (yes, stationary)
stochastic process with LTP.
Amazingly, Kolmogorov studied the
stochastic process that describes this behaviour, discovered by Hurst
in geophysics, 10 years earlier (1940).
There is some evidence that I will be presenting
in the next article, that this could be the case, and small and slow forcing changes could be responsible for climate changes that can not be attributed to
stochastic processes, given their regularity.
In particular, What if macroscopic evolution is not just another «a cultural consensus» imposed by like minded atheists / materialists who by definition preclude open science of testing it against the null hypothesis of known
stochastic and chemical
processes (as distinct from mutations causing microevolution)?
However, if the information
in that sample period is statistically consistent only with a
stochastic I (1)
process then there is no valid reason provided by the data alone to have any confidence that «trend» can be projected to other periods.
«The false assumption is that the period 1880 — 1935 is purely governed by
stochastic processes, whereas
in reality there as already a change
in climate forcing
in that period (from solar, volcanic and GHG).»