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Topic: Gaussian stochastic process

Related Topics

Gaussian function

Stochastic process

Normally distributed and uncorrelated does not imply independent

Wiener process

Normal distribution

Probability density function

Bernoulli distribution

Probability theory

Fuzzy logic

Scalar

Flux

Photon

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	Stochastic process - Wikipedia, the free encyclopedia
		In practical applications, the domain over which the function is defined is a time interval (a stochastic process of this kind is called a time series in applications) or a region of space (a stochastic process being called a random field).
		Stochastic processes may be defined in higher dimensions by attaching a multivariate random variable to each point in the index set, which is equivalent to using a multidimensional index set.
		Gaussian processes: processes where all linear combinations of coordinates are normally distributed random variables.
	en.wikipedia.org /wiki/Stochastic_process (1411 words)

	Stochastic process -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-03)
		Stochastic processes may be defined in higher dimensions by attaching a (Click link for more info and facts about multivariate random variable) multivariate random variable to each point in the index set, which is equivalent to using a multidimensional index set.
		The paradigm continuous stochastic process is that of (The random motion of small particles suspended in a gas or liquid) Brownian motion.
		Homogeneous processes: processes where the domain has some ((mathematics) an attribute of a shape or relation; exact correspondence of form on opposite sides of a dividing line or plane) symmetry and the finite-dimensional probability distributions also have that symmetry.
	www.absoluteastronomy.com /encyclopedia/s/st/stochastic_process.htm (1638 words)

	Gaussian process - Wikipedia, the free encyclopedia
		The Ornstein-Uhlenbeck process is a stationary Gaussian process.
		The Brownian bridge is a Gaussian process whose increments are not independent.
		Inference of continuous values with a Gaussian process prior is known as Gaussian process regression.
	en.wikipedia.org /wiki/Gaussian_process (242 words)

	Prosés stokastik - Wikipédia
		In practical applications, the domain over which the function is defined is a time interval (a stochastic process of this kind is called a deret waktu in applications) or a region of space (a stochastic process being called a random field).
		The domain D becomes the index set of the stochastic process, and a particular stochastic process is determined by specifying the joint probability distributions of the various random variables f(x).
		Note, however, that the definition of stochastic process as an indexed collection of random variables is much more general than the case where the indices are points of the domain of the random function.
	su.wikipedia.org /wiki/Stochastic_process (1565 words)

	Wiener process - Wikipedia, the free encyclopedia
		In mathematics, the Wiener process, so named in honor of Norbert Wiener, is a continuous-time Gaussian stochastic process with independent increments used in modelling Brownian motion and some random phenomena observed in finance.
		Geometric Brownian motion, one example of which is the Black-Scholes asset pricing model, is a stochastic process which is used to model processes that can never take on negative values, such as the value of stocks.
		The Wiener process has an analytic representation as a sine series whose coefficients are independent Gaussian random variables of mean 0 and variance 1.
	en.wikipedia.org /wiki/Wiener_process (276 words)

	Encyclopedia: Brownian motion
		Brownian motion is among the simplest stochastic processes on a continuous domain, and it is a limit of both simpler (see random walk) and more complicated stochastic processes.
		Brownian motion is related to the random walk problem and it is generic in the sense that many different stochastic processes reduce to Brownian motion in suitable limits.
		In fact, the Wiener process is the only time-homogeneous stochastic process with independent increments that has continuous trajectories.
	www.nationmaster.com /encyclopedia/Brownian-motion (1845 words)

	Stochastic process: Definition and Links by Encyclopedian.com - All about Stochastic process
		processes where the domain has some symmetry and the finite-dimensional probability distributions also have that symmetry.
		They can be modelled as stochastic processes where the domain is a sufficiently large family of subsets of S, ordered by inclusion; the range is the set of natural numbers; and, if A is a subset of B, f(A) ≤ f(B) with probability 1.
		processes where all linear combinations of coordinates are Gaussian random variables.
	www.encyclopedian.com /st/Stochastic-process.html (959 words)

	Generalized Stochastic Subdivision
		Stochastic techniques have assumed a prominent role in computer graphics, because of their success in modeling a variety of complex and natural phenomena.
		Since the Gaussian autocorrelation function possesses all derivatives, a random process having this autocorrelation is analytic, suggesting that deterministic interpolation may be used at scales where the determinant of R is zero.
		The small-scale behavior of the noise is governed by the behavior of the autocorrelation function near the origin (as we saw in the preceding remarks on the derivatives of random processes) or equivalently by the high-frequency portion of the spectrum.
	www.idiom.com /~zilla/Work/Gsd/gsd.html (8116 words)

	Normal distribution - Wikipedia, the free encyclopedia
		It is a family of distributions of the same general form, differing in their location and scale parameters: the mean ("average") and standard deviation ("variability"), respectively.
		The overwhelming biological evidence is that bulk growth processes of living tissue proceed by multiplicative, not additive, increments, and that therefore measures of body size should at most follow a lognormal rather than normal distribution.
		In particular, the entries for "normal" (distribution) by John Aldrich, "Gaussian", and "Error, law of error, theory of errors, etc.".
	en.wikipedia.org /wiki/Normal_distribution (4114 words)

	Stochastic Process
		A continuous-time process is called white noise if for arbitrary n, sampling at arbitrary time instants t_1, t_2,..., t_n, the resulting random variables, X_{t_1}, X_{t_2},..., X_{t_n} are independent, i.e., their joint pdf f(x_1, x_2,..., x_n)= f(x_1)f(x_2)...*f(x_n).
		the queue in M/M/1 is a Markov process.
		the queue in M/G/1 and G/M/1 is a semi-Markov process.
	www-2.cs.cmu.edu /~dpwu/books/math/probability/StochasticProcess.html (2015 words)

	NTU Info Centre: Stochastic process (Site not responding. Last check: 2007-11-03)
		A stochastic process is an indexed collection of random variables, each of which is defined on the same probability space "W" and takes values on the same codomain D (often the reals R).
		Then, a function f : N → R is a sequence of real numbers, and a stochastic process with domain N and range R is a random sequence.
		Gaussian processs: processes where all linear combinations of coordinates are normally distributed random variables.
	www.nowtryus.com /article:Stochastic_processes (1368 words)

	Publications List
		Boltzmann machines are undirected graphical models with two-state stochastic variables, in which the logarithms of the clique potentials are quadratic functions of the node states.
		The original derivation of a deterministic algorithm relied on the use of a Gaussian approximating distribution with a diagonal covariance matrix and hence was unable to capture the posterior correlations between parameters.
		However, the derivation of a deterministic algorithm relied on the use of a Gaussian approximating distribution with a diagonal covariance matrix and so was unable to capture the posterior correlations between parameters.
	www.research.microsoft.com /~cmbishop/publications_abs.htm (13697 words)

	List of publications
		A remark on the increment of a Wiener process.
		Convergence of integrals of uniform empirical and quantile processes.
		A Gaussian correlation inequality and its application to the existence of small ball constant.
	darkwing.uoregon.edu /~qmshao/pub/pub.htm (1401 words)

	Stochastic Processes (Site not responding. Last check: 2007-11-03)
		This popular model is the most used stochastic process in financial economics theory and in the practice.
		The stochastic process of V, geometric Brownian motion (GBM), means that this variable follows a lognormal process over time with the following parameters.
		The ease of using irregularly sampled data is one of the greatest advantages of continuous-time stochastic processes, by the econometric point of view.
	www.puc-rio.br /marco.ind/stochast.html (1792 words)

	Strategy and model building in the fourth dimension: a null model for genotype x age interaction as a Gaussian ... (Site not responding. Last check: 2007-11-03)
		Strategy and model building in the fourth dimension: a null model for genotype x age interaction as a Gaussian stationary stochastic process.
		BACKGROUND: Using univariate and multivariate variance components linkage analysis methods, we studied possible genotype x age interaction in cardiovascular phenotypes related to the aging process from the Framingham Heart Study.
		CONCLUSIONS: There is polygenic genotype x age interaction for fasting glucose and systolic blood pressure and quantitative trait locus x age interaction for a linkage signal for systolic blood pressure phenotypes located on chromosome 17 at 67 cM.
	www.arclab.org /medlineupdates/abstract_14975102.html (148 words)

	Citations: Non-Gaussian State Space Modeling of Nonstationary Time Series - Kitagawa (ResearchIndex) (Site not responding. Last check: 2007-11-03)
		The idea is to model the underlying classes (bottle features) as a Markov process, that is P (K t jK 1 ; K t Gamma1) P (K t jK t Gamma1) memory only lasts one step.
		Mariano and Brown (1983,1989) and Brown and Mariano (1984,1989) suggested using Monte Carlo stochastic simulations for the expectation of a nonlinear function.
		Gaussian sum approximation [3] is an early research.
	citeseer.ist.psu.edu /context/296250/0 (2858 words)

	Stochastic Processes: Appendix A (Site not responding. Last check: 2007-11-03)
		That is, they are event-driven processes (evolve only if a new investment in information is performed) and not time-driven processes as most stochastic processes, which evolve with the pure passage of time.
		By counting process point of view, N(0) = 0 (the number of jumps in the process N is zero at t = 0).
		Karlin and Taylor ("A Second Course in Stochastic Processes", Academic Press, 1981), p.432, states "The general Lévy process can be represented as a sum of a Brownian motion, a uniform translation, and a limit (actually, an integral) of a one-parameter family of compound Poisson processes, where all the contributing basic processes are mutually independent".
	www.puc-rio.br /marco.ind/stoch-a.html (4253 words)

	Edinburgh Research Archive : Item 1842/292 (Site not responding. Last check: 2007-11-03)
		Gaussian noise models are appealing as they usually result in noise suppression algorithms that are simple: i.e.
		However, such linear techniques may be sub-optimal when the noise process is either a non-Gaussian stochastic process or a chaotic deterministic process.
		In the event of encountering such noise processes, improvements in noise suppression, relative to the performance of linear methods, may be achievable using nonlinear signal processing techniques.
	hdl.handle.net /1842/292 (202 words)

	INFORMS 1954- Lanchester Awards
		Stochastic games, which generalize Markov decision processes, were introduced in 1953.
		Stochastic process limits have become a standard tool in operations research to study queues arising from complex systems like communication networks.
		One can often derive mathematical expressions for the transforms of distributions that characterize performance of a stochastic system model, but solutions in the transform domain have long been viewed as unsatisfactory, at least partly because numerical inversion of the transforms was considered impractical.
	www.informs.org /Prizes/LanchesterDetails.html (12185 words)

	Stochastic_Process (Site not responding. Last check: 2007-11-03)
		Any process which may be described in terms of probabilities.
		In such a process, although the details of individual events are unpredictable, the overall character or behaviour of the system will be.
		Natural processes, such as rain falling, the motion of groups of insects or birds, or the random movement of smoke particles in air may be described as stochastic.
	www.sfu.ca /sonic-studio/handbook/Stochastic_Process.html (86 words)

	A FAMILY OF RECURSIVE ALGORITHMS FOR CHANNEL IDENTIFICATION IN ALPHA-STABLE NOISE (Site not responding. Last check: 2007-11-03)
		The optimisation criterion in Gaussian noise environment is often the minimisation of a quadratic function of the estimation error.
		The main difference between the non-Gaussian stable distribution and the Gaussian distribution is that the tails of the stable density are heavier than those of the Gaussian density.
		This characteristic of the stable distribution is one of the main reasons why the stable distribution is suitable for modelling signals and noise of impulsive nature.
	www.ee.ed.ac.uk /~atg/academic/paper_Bayona99/paper.html (1656 words)

	Department of Statistics (Site not responding. Last check: 2007-11-03)
		The graph of a Gaussian stochastic process, regarded as a subset of the plane, has a fractal dimension lying between 1 and 2.
		The fractal dimension depends on the underlying smoothness of the process, with smoother processes having a lower dimension.
		In this talk we shall explore why the accuracy of the estimator deteriorates if the underlying process is too smooth, and we propose a family of new estimators which do have the desired accuracy.
	www.amsta.leeds.ac.uk /Statistics/seminars/kent.html (156 words)

	Nonlinear System Identification (Site not responding. Last check: 2007-11-03)
		The identification problem is examined in a stochastic setup where the input is a white Gaussian stochastic process with known intensities.
		Extension of these results to the case of more general qudratic models and more general stochastic input signals is the subject of ongoing research.
		Current research is focused on the problem of deriving sufficient conditions for persistence of excitation of the input signal and on the extension of the results to more general quadratic ARMA models.
	cgi.di.uoa.gr /~kalou/projects/nlid.html (241 words)

	Monte Carlo Simulation of Stochastic Processes (Site not responding. Last check: 2007-11-03)
		The jump process dq is assumed to be independent of the continuous stochastic increment dz.
		The stochastic process for the commodity price P(t) is chosen so that the commodity prices are function of x(t) described by the first equation of this item.
		For geometric Brownian process combined with jumps there is no problem because the process drift doesn't depend on the current level of the stochastic variable (it is possible even to use Brownian bridge with independent simulations for each process).
	www.puc-rio.br /marco.ind/sim_stoc_proc.html (4703 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		This is a bilinear transformation which maps a function of one variable (time) to a function of two variables which can be interpreted as a simultaneous distribution over time and frequency of the function's energy.
		Using stochastic integration it is possible to define the Wigner-Ville distribution of a continuous-time Gaussian stochastic process.
		We describe a condition on the process covariance function, namely it should be a member of a function space called Feichtinger's algebra, which is sufficient to ensure the Wigner-Ville distribution of the process has finite variance.
	www.maths.lth.se /matstat/seminar/s04/s040305.txt (139 words)

	PASCAL -
		The main aim of this talk is to raise the issue of the consistency of Gaussian Process (GP) predictors with the other workshop participants. GP prediction works by placing a stochastic Gaussian process prior over functions and conditioning this on observations in order to make predictions.
		In both the regression case (Gaussian noise) and the classification case (logistic link function) the posterior is unimodal.
		In the regression case the posterior is again a Gaussian process, but this is not so in the classification case.
	eprints.pascal-network.org /archive/00000594 (240 words)

	Dissertation (Site not responding. Last check: 2007-11-03)
		The basic problem of groundwater pollutant remediation by well pumping was modeled as a dicrete-time LQG (linear state dynamics, quadratic costs, Gaussian stochastic process) optimal control problem.
		This remediation process is modeled by a system of equations representing the flow transport/diffusion, the diffusion and dispersion of the contaminant, and the aquifer flow.
		There is also a stochastic process going on, due to small fluctuations in the contaminant concentration and hydraulic head due to leekage, seepage, etc.
	www.ima.umn.edu /~dkern/thesis.html (473 words)

	Stochastic Realization and Identification
		One of the research themes of the Systems Theory Group at LADSEB is Stochastic Realization and its main object is to construct finite dimensional representations of an infinite (or, in practice, very long) sequence of random variables, called stochastic processes.
		More precisely, if y(t) is a linear gaussian stochastic process, any Markov process x(t) which makes the past and future of y conditionally independent is called a state of the process.
		Therefore the tools are essentially mathematical and they encompass theory of stochastic processes, linear algebra and, above all, functional analysis.
	www.ercim.org /publication/Ercim_News/enw40/gombani.html (470 words)

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