
	Where results make sense

Topic: Stationary ergodic process

	Discrete sample paths
		This book is about finite-alphabet stationary processes, which are important in physics, engineering, and data compression.
		The focus is on the combinatorial properties of typical finite sample paths drawn from a stationary, ergodic process.
		A secondary goal is to give a careful presentation of the many models for stationary finite-alphabet processes that have been developed in probability theory, ergodic theory, and information theory.
	www.math.utoledo.edu /~pshields/ergodic.html (121 words)

	Philosophy of Statistical Mechanics
		Further, it became apparent that this spontaneous approach to equilibrium was a time-asymmetric process.
		With ergodicity we can show that the standard probability distribution is the only one that is so invariant, at least if we confine ourselves to probability measures that assign probability zero to every set assigned zero by the standard measure.
		If we assume that probability measures assigning non-zero probability to sets of states assigned zero by the usual measure can be ignored, then we can show that the standard probability is the only such time invariant probability under the dynamics that drives the individual systems from one microscopic state to another.
	plato.stanford.edu /entries/statphys-statmech (5119 words)

	Preface: Discrete sample paths
		An important and simple class of such models is the class of concatenated-block processes, that is, the processes obtained by independently concatenating fixed-length blocks according to some block distribution and randomizing the start.
		Of particular note in the discussion of process models is how ergodic theorists think of a stationary process, namely, as a measure-preserving transformation on a probability space, together with a partition of the space.
		Properties related to entropy which hold only for restricted classes of processes are discussed in Chapter III, including rates of convergence for frequencies and entropy, the estimation of joint distributions in both the variational metric and the dbar-metric, a connection between entropy and dbar-neighborhoods, and a connection between entropy and waiting times.
	www.math.utoledo.edu /~pshields/preface.html (1104 words)

	Applications of Heavy Tailed Distributions in Economics, Engineering and Statistics
		The Harmonizable Fractional Stable Motion, which is a complex-valued, stable, self-similar process with stationary increments, is one of the many different extensions of fractional Brownian motion to the stable case.
		In some cases the sample acf may converge to a random limit (even when the process is ergodic) which casts serious doubt on the reliability of statistical methods which use the sample acf.
		For any stationary ergodic process with finite absolute mean we define (through a ratio of expectations) the autocovariation (a generalization of the covariation).
	academic2.american.edu /~jpnolan/HeavyTailsConference/HeavyTailsProgram.html (11476 words)

	Information_theory
		The appropriate measure for this is the transinformation, and this maximum transinformation is called the channel capacity and is given by:
		Any process that generates successive messages can be considered a source of information.
		Sources can be classified in order of increasing generality as memoryless, ergodic, stationary, and stochastic.
	www.brainyencyclopedia.com /encyclopedia/i/in/information_theory.html (3247 words)

	Refereed Publications Authored by Kieffer, John C.
		Kieffer, John C. ``On obtaining a stationary process isomorphic to a given process with a desired distribution.'' Monatsh.
		Kieffer, John C. ``On coding a stationary process to achieve a given marginal distribution.'' Ann.
		Kieffer, J. ``On the approximation of stationary measures by periodic and ergodic measures.'' Ann.
	www.ee.umn.edu /users/kieffer/citations2.html (1268 words)

	Statistical Laboratory Seminars
		In the simplest model, the route followed by the data packets and the acknowledgements of the controlled connection is modeled by a series of infinite capacity FIFO queues, each of which receives in addition some cross traffic represented by an exogenous flow.
		We investigate the stability region of the system under general stochastic assumptions, that is stationary and jointly ergodic input processes.
		The notion of stochastic process on manifold is applied to various physically appealing circumstances, in order to study the approach to thermal equilibrium for a given initial quantum state.
	www.statslab.cam.ac.uk /Seminars/statsemeast1998.html (946 words)

	Home 2
		The book is written with practitioners in mind, and many of the problems addressed and the solutions presented are relevant not only to the isolation of stationary sensitive equipment (the main thrust of the book), but also to civil engineering and transport applications.
		Comments: This volume is an offspring of the special semester "Ergodic Theory, Geometric Rigidity and Number Theory" held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from January to July, 2000.
		The emphasis of the book is on the active control of waves in structures, the active isolation of vibrations, the use of distributed strain actuators and sensors, and the active control of structurally radiated sound.
	www.iiav.org /books1.htm (10096 words)

	ASP FY97 Annual Scientific Report
		Schimel, D. S., VEMAP Participants, and B. Braswell, 1997: Continental scale variability in ecosystem processes*: Models, data, and the role of disturbance.
		Trenberth, K. E., 1997: Physical processes involved in changes of extremes of the hydrological cycle with climate change.
		Zou, X., 1997: Tangent linear and adjoint of "on-off" processes and their feasibility for use in four-dimensional variational data assimilation.
	www.ncar.ucar.edu /ASR97/pub.html (15099 words)

	Ergodic properties of Poissonian ID processes
		We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its Lévy measure.
		The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity.
		To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson measure, which, more generally, has led us to study basic ergodic properties of these objects.
	projecteuclid.org /euclid.aop/1175287754 (201 words)

	Large Deviations
		Similar large deviation principles can be stated for the empirical distribution, the empirical process, functionals of sample paths, etc., rather than just the empirical mean.
		Since ergodic theory extends the probabilistic limit laws to stochastic processes, rather than just sequences of independent variables, it shouldn;t be surprising that large deviation principles also hold for some stochastic processes.
		There are also important connections to information theory, since in an awful lot of situations, the large deviations rate function is the Kullback-Leibler divergence, a.k.a.
	cscs.umich.edu /~crshalizi/notebooks/large-deviations.html (1729 words)

	Nonparametric inference for ergodic, stationary time series
		The setting is a stationary, ergodic time series.
		The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability of the next observation, given the infinite past.
		ROUSSAS, G. Non-parametric estimation of the transition distribution of a Markov process.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1033066215 (352 words)

	Dept. of Mathematics, Graduate School of Science and School of Science, Osaka Univ.
		It seems to me that complex manifolds are not metallically hard but have common warm feeling with wood or bamboo, which have grain and gnarl.
		Analytic continuations, as you learned in the course on the function theory of complex variables, is analogous to the process of growth of plants.
		For data compression, assuming a sequence has been emitted from a stationary ergodic process, we predict the future data based on the law of large numbers.
	www.sci.osaka-u.ac.jp /introduction/eng/math.html (9444 words)

	subadditive ergodic theorem
		Definition: If a stationary and ergodic process satisfies the subadditive inequality, it grows almost surely linearly in time.
		HTML page formatted Mon Sep 11 09:46:08 2006.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "subadditive ergodic theorem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/subadditive.html (117 words)

	Statistics & Probability - Course Info (Site not responding. Last check: 2007-10-21)
		General Theory of Processes: Weak Convergence and the General Theory of Processes
		Dynkin, E.B. Markov Processes I and II Academic
		Williams, D. and Rogers, L.C.G. Diffusions, Markov Processes, and Martinglaes Vol.
	www.stt.msu.edu /katz_author.asp (2980 words)

Try your search on: Qwika (all wikis)