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Type of random process
In probability a quasi-stationary distribution is a random process that admits one or several absorbing states that are reached almost surely, but is
Quasi-stationary_distribution
Class of stochastic process
mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process
Stationary_process
Statistical simulation method
KMC as a coarse-graining of the Langevin dynamics using the quasi-stationary distribution approach has been developed by T. Lelièvre and collaborators
Kinetic_Monte_Carlo
Form of solution in probability theory
computed assuming independent marginal distributions, which can give a good approximation to the stationary distribution under some conditions. Semi-product-form
Product-form_solution
Wigner distribution function in physics as opposed to in signal processing
de Broglie–Bohm causal trajectories. Basil Hiley has shown that the quasi-probability distribution may be understood as the density matrix re-expressed in terms
Wigner quasiprobability distribution
Wigner_quasiprobability_distribution
Calculation of complex statistical distributions
{\displaystyle \pi } denote the stationary distribution and P t ( x , ⋅ ) {\displaystyle P^{t}(x,\cdot )} the distribution of the Markov chain after t {\displaystyle
Markov_chain_Monte_Carlo
Journal, 28 (5), 817–843. Ferrari, Pablo A.; Mari, Nevena "Quasi stationary distributions and Fleming Viot processes" Archived 2016-03-03 at the Wayback
Fleming–Viot_process
Statistical model
variables has a multivariate normal distribution. The distribution of a Gaussian process is the joint distribution of all those (infinitely many) random
Gaussian_process
Quantity in solid state thermodynamics
pulse, the electron distribution cannot be described by any thermal distribution. One cannot define the quasi-Fermi level or quasi-temperature in this
Fermi_level
Mathematical function for the probability a given outcome occurs in an experiment
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more
Probability_distribution
Active galactic nucleus (AGN) containing a supermassive black hole
extremely luminous active galactic nucleus (AGN). It is sometimes known as a quasi-stellar object, abbreviated QSO. The emission from an AGN is powered by
Quasar
can be considered as quasi-birth-death processes with infinitely (but countably) many phases. The stationary distribution of a quasi-birth-death process
Quasi-birth–death_process
Measure of variation in statistics
known to be non-stationary series, whereas the statistical calculations above, such as standard deviation, apply only to stationary series. To apply
Standard_deviation
Part of signal processing in time-frequency analysis
way of comparison: Wigner quasi-probability distribution, also called the Wigner function or the Wigner–Ville distribution). Given the shared algebraic
Wigner_distribution_function
Dynamical group of trans-Neptunian objects
Neptune's orbital period (holding Neptune stationary). Pluto is grey, Orcus is red, and Neptune is the white (stationary) dot at 5 o'clock. Uranus is blue, Saturn
Plutino
Highest particle energy in a Fermi gas at absolute zero
statistics: the distribution of electrons over stationary states for non-interacting fermions at non-zero temperature. Fermi level Quasi Fermi level The
Fermi_energy
Statistical method
Bootstrapping is a procedure for estimating the distribution of an estimator by resampling (often with replacement) one's data or a model which is estimated
Bootstrapping_(statistics)
Fundamental theorem in probability theory and statistics
distribution to N(0,1) as n→ ∞. Lemma—Suppose X 1 , X 2 , … {\displaystyle X_{1},X_{2},\dots } is a sequence of real-valued and strictly stationary random
Central_limit_theorem
Probabilistic problem-solving algorithm
will be samples from the desired (target) distribution. By the ergodic theorem, the stationary distribution is approximated by the empirical measures
Monte_Carlo_method
software Static analysis Stationary distribution Stationary ergodic process Stationary process Stationary sequence Stationary subspace analysis Statistic
List_of_statistics_articles
Brazilian physicist of Greek descent
(Brazilian Journal of Physics 29, 1;Figure 4): That a longstanding quasi-stationary state (QSS) was expected in long-range interacting Hamiltonian systems
Constantino_Tsallis
Nonparametric measure of rank correlation
necessary. This method is applicable to stationary streaming data as well as large data sets. For non-stationary streaming data, where the Spearman's rank
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Mathematical model
Markov reward model with boundary conditions. The stationary distribution is a phase-type distribution as first shown by Asmussen and can be computed using
Fluid_queue
chromatography that uses a liquid stationary phase that is held in place by inertia of the molecules composing the stationary phase accelerating toward the
Countercurrent_chromatography
Method of estimating the parameters of a statistical model, given observations
such as generalized linear models. Although popular, quasi-Newton methods may converge to a stationary point that is not necessarily a local or global maximum
Maximum_likelihood_estimation
further simplified by taking advantage of the quasi-stationary state in welding, where temperature distribution from the perspective of a coordinate system
Moving heat source model for thin plates
Moving_heat_source_model_for_thin_plates
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation σ
Coefficient_of_variation
Object with trapped electrical charge
"electricity" and -et from "magnet") is a dielectric material that has a quasi-permanent electrical polarisation. An electret has internal and external
Electret
characterize the equilibrium distribution (or any stationary distribution) of a Markov chain, when such a distribution exists. For a continuous time
Balance_equation
Invariant measure that displays a less restricted form of ergodicity
stating that μ {\displaystyle \mu } equals the zero-noise limit stationary distribution of a Markov chain with states T i ( x ) {\displaystyle T^{i}(x)}
Sinai–Ruelle–Bowen_measure
Algorithm used by Google Search to rank web pages
changes its operational mode can be described by transitions between quasi-stationary states in correlation structures of traffic flow. PageRank has been
PageRank
Statistical property of collections of time series data
or more time series variables, even if the individual series are non-stationary (i.e., they contain stochastic trends). In such cases, the variables may
Cointegration
Correlation of a signal with a time-shifted copy of itself, as a function of shift
models incorporate autocorrelation, such as unit root processes, trend-stationary processes, autoregressive processes, and moving average processes. In
Autocorrelation
Set of nonlinear waves deviated far from thermal equilibrium
assumptions and describing the wave system by kinetic equations and their stationary solutions – the approach developed by Vladimir E. Zakharov. These solutions
Wave_turbulence
Statistical model
Whittle likelihood is an approximation to the likelihood function of a stationary Gaussian time series. It is named after the mathematician and statistician
Whittle_likelihood
Darwinian evolution of self-replicating entities within framework of physical chemistry
related genotypes that exist in an environment of high mutation rate (at stationary state), where a large fraction of offspring are expected to contain one
Quasispecies_model
Time series statistical test
is present if ρ = 1 {\displaystyle \rho =1} . The model would be non-stationary in this case. The regression model can be written as Δ y t = ( ρ − 1 )
Dickey–Fuller_test
Concept in game theory
that opponents are using stationary (possibly mixed) strategies, and responds optimally to the historical empirical distribution of their opponents' past
Fictitious_play
Statistic for rank correlation
correlation coefficient based on coarsening the joint distribution of the random variables. Non-stationary data is treated via a moving window approach. This
Kendall rank correlation coefficient
Kendall_rank_correlation_coefficient
Method to solve constrained optimization problems
the equality constraint g ( x ) = 0 {\displaystyle g(x)=0} , find the stationary points of L {\displaystyle {\mathcal {L}}} considered as a function of
Lagrange_multiplier
Constant capital and population size
increasing rapidly — society would finally "... attain the conditions of a quasi-stationary community where change and progress would result only from changes
Steady-state_economy
Ratio of active power to apparent power
electromechanical instrument is the polarized-vane type. In this instrument a stationary field coil produces a rotating magnetic field, just like a polyphase motor
Power_factor
Random motion of particles suspended in a fluid
one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs frequently in pure and applied mathematics
Brownian_motion
Sequence of data points over time
Diagnosis Methodology Based on Non-Stationary Monitoring Signals by Extracting Features With Unknown Probability Distribution". IEEE Access. 8: 59821–59836
Time_series
Theorem of stationary processes
Wiener–Khinchin theorem), named after Herman Wold, says that every covariance-stationary time series Y t {\displaystyle Y_{t}} can be written as the sum of two
Wold's_theorem
Statistical ensemble of particles in thermodynamic equilibrium
to name quasi-equilibrium chemical potentials which can differ among the different populations. Examples: (semiconductor physics) distinct quasi-Fermi levels
Grand_canonical_ensemble
Statistical distribution for dependence between random variables
cumulative distribution function with marginal distributions F i ( x ) {\displaystyle F_{i}(x)} . Copulas mainly work when time series are stationary and continuous
Copula_(statistics)
Statistical technique to aid interpretation of data
that the errors are non-stationary, then the non-stationary series { y t } {\displaystyle \{y_{t}\}} is called trend-stationary. The least-squares method
Linear_trend_estimation
Function related to statistics and probability theory
stationary points of the log-likelihood of independent events than for the likelihood of independent events. The equations defined by the stationary point
Likelihood_function
well as other theories. quasi-linear convective system (QLCS) See squall line. quasi-stationary front A front that is stationary or nearly so; conventionally
Glossary_of_meteorology
Geology of fourth planet from the Sun
number of basin-sized structures previously hidden in visual images. Called quasi-circular depressions (QCDs), these features likely represent derelict impact
Geology_of_Mars
Method of analysis in probability theory
each of B00, B01, B10, A0, A1 and A2 are matrices. To compute the stationary distribution π writing π Q = 0 the balance equations are considered for sub-vectors
Matrix_geometric_method
Aspects of fluid mechanics involving fluid flow
in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow
Fluid_dynamics
Statistical model used in time series analysis
autoregressive–moving-average (ARMA) model is used to represent a (weakly) stationary stochastic process by combining two components: autoregression (AR) and
Autoregressive moving-average model
Autoregressive_moving-average_model
Property of measure-preserving dynamical systems
its joint distribution defines a probability measure on the path space S N {\displaystyle S^{\mathbb {N} }} . The process is stationary if this probability
Ergodicity
considered in isolation is quasireversible, always has a product form stationary distribution. Quasireversibility had been conjectured to be a necessary condition
Quasireversibility
Mathematical technique used to solve a certain class of partial differential equations
space, whereas moments of the distribution such as densities and currents are computed simultaneously on Eulerian (stationary) mesh points. PIC methods were
Particle-in-cell
Subfield of set theory
for every regular cardinal κ>ω there are no ordinal definable disjoint stationary subsets of κ made of ordinals of cofinality ω. The consistency strength
Determinacy
Process by which atoms or molecules acquire charge by gaining or losing electrons
{\alpha } (t)} ). From here one can apply Floquet theory to calculate quasi-stationary solutions of the TDSE. In high frequency Floquet theory, to lowest
Ionization
Statistics concept
estimating the cross-covariance of a pair of signals that are wide-sense stationary, missing samples do not need be random (e.g., sub-sampling by an arbitrary
Estimation of covariance matrices
Estimation_of_covariance_matrices
Signal processing algorithm
in such fields as optics as the principle of stationary phase, which states that for periodic or quasi-periodic signals, the variation of the Fourier
Reassignment_method
Wave where gravity is the main restoring force
phase-speed derivation The gravity wave represents a perturbation around a stationary state, in which there is no velocity. Thus, the perturbation introduced
Gravity_wave
Principle in kinetic systems
process or reversible Markov chain if there exists a positive stationary distribution π that satisfies the detailed balance equations π i P i j = π j
Detailed_balance
Covariance and correlation
individually wide-sense stationary) conveyed by the requirement that ( X t , Y t ) {\displaystyle (X_{t},Y_{t})} are jointly wide-sense stationary. The cross-correlation
Cross-correlation
Anomalous diffraction at metallic gratings
Fano, U. (1941). "The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld's Waves)". Journal of the Optical
Wood's_anomaly
Swedish American mathematician (1923–2016)
Chelsea. Grenander, Ulf; Rosenblatt, M (1957). Statistical Analysis of Stationary Time Series. American Mathematical Society. ISBN 978-0-8284-0320-7. {{cite
Ulf_Grenander
Matter and radiation in the space between the star systems in a galaxy
lines caused by the orbital motion of the spectroscopic binary star". The stationary nature of the line led Hartmann to conclude that the gas responsible for
Interstellar_medium
State of thermodynamic systems where no net flow of matter or energy occurs
its local Maxwell–Boltzmann distribution of molecular velocities. A global non-equilibrium state can be stably stationary only if it is maintained by
Thermodynamic_equilibrium
Theory of gravitation as curved spacetime
general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond
General_relativity
Statistical hypothesis test for forecasting
series is a stationary process, the test is performed using the level values of two (or more) variables. If the variables are non-stationary, then the test
Granger_causality
Optimization technique
propose a simplex heuristic, which was shown by Powell to converge to non-stationary points on some problems. 1965: Ingo Rechenberg discovers the first Evolution
Metaheuristic
Statistical model validation technique
structure of the system being studied evolves over time (i.e. it is "non-stationary"). Both of these can introduce systematic differences between the training
Cross-validation_(statistics)
Signal processing technique
periodogram. By contrast, the parametric approaches assume that the underlying stationary stochastic process has a certain structure that can be described using
Spectral_density_estimation
Blazar in the constellation of Fornax
variability of the flares were caused by emission region interactions through stationary shock waves. It is suggested PKS 0346−27 is a very-high energy emitter
PKS_0346−27
Matrix of second derivatives
{\displaystyle \mathbf {x} ,} then f {\displaystyle f} has a critical point (or stationary point) at x . {\displaystyle \mathbf {x} .} The determinant of the Hessian
Hessian_matrix
Soviet mathematician (1903–1987)
Kolmogorov "established the basic theorems for smoothing and predicting stationary stochastic processes"—a paper that had major military applications during
Andrey_Kolmogorov
Subfield of information theory and computer science
knowledge of the probability distribution (e.g., whether it is independent and identically distributed, Markovian, or even stationary). In this way, AIT is known
Algorithmic information theory
Algorithmic_information_theory
Rapid climate fluctuation in the last glacial period
fluctuations). Dansgaard et al. speculate that these may be related to quasi-stationary modes of the atmosphere-ocean system. D-O events tend to be what drives
Dansgaard–Oeschger_event
Relations between flows and forces, or gradients, in thermodynamic systems
{\displaystyle \beta _{ik}} is a positive definite symmetric matrix. Using the quasi-stationary equilibrium approximation, that is, assuming that the system is only
Onsager_reciprocal_relations
Branch of mathematics that studies dynamical systems
associated with a sequence of i.i.d. random variables and some more general stationary processes follows from Kolmogorov's zero–one law. Ergodicity of a continuous
Ergodic_theory
British multinational oil and gas company
state lawmakers: "[Initiative 1631] would exempt six of the ten largest stationary source emitters in the state, including a coal-fired power plant, an aluminum
BP
Measure of a system's order
and this definition applies for both classical and quantum version. For stationary (equilibrium) system, the time origin is irrelevant, and C A B ( τ ) =
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Algorithm that estimates unknowns from a series of measurements over time
Consider a truck on frictionless, straight rails. Initially, the truck is stationary at position 0, but it is buffeted this way and that by random uncontrolled
Kalman_filter
School of thought in economics
classical economists. However, John Stuart Mill believed that a future stationary state of a constant population size and a constant stock of capital was
Classical_economics
Electrical transmission without physical connection
fields are created by charged particles in matter such as electrons. A stationary charge creates an electrostatic field in the space around it. A steady
Wireless_power_transfer
American mathematician (1931-2012)
less simultaneously by Dynkin and Yushkevich in the Soviet Union) and the quasi-left continuity of the sample paths of the process. In addition, his thesis
Robert_McCallum_Blumenthal
Statistical indicators in signal processing
However, the Fourier transform is not appropriate for analysing non-stationary signals in which textures are irregular or non-uniform. Short time Fourier
Hjorth_parameters
Device that changes direct current (DC) to alternating current (AC)
depending on circuit design. Common types of inverters produce square waves or quasi-square waves. One measure of the purity of a sine wave is the total harmonic
Power_inverter
Well in the Masjid al-Haram in Mecca
come in several variants, chilled and unchilled, as well as being either stationary or worn as a backpack by employees of the complexes with disposable plastic
Zamzam_Well
Special type of continuous-time Markov process
standard birth-and-death process. Erlang unit Queueing theory Queueing models Quasi-birth–death process Moran process Feller, William (1939). "Die Grundlagen
Birth–death_process
Quantum physics terminology
time, are often considered unstable bound states as well and are called "quasi-bound states". Examples include radionuclides and Rydberg atoms. In relativistic
Bound_state
Statistical experiment designs
Since UDD random walks are regular Markov chains, they generate a stationary distribution of dose allocations, π {\displaystyle \pi } , once the effect of
Up-and-down_design
Time series model
(MF2-GARCH) was proposed by Conrad and Engle (2025), and it features stationary returns and allows for recursive long-term volatility forecasts. They
Autoregressive conditional heteroskedasticity
Autoregressive_conditional_heteroskedasticity
Chinese economist
of copula-based semiparametric stationary Markov time series models that contains nonparametric marginal distributions and parameterized copulas. Chen
Xiaohong_Chen
Natural satellite orbiting Earth
of time but then alter in the long term (Morais et al, 2002). These are quasi-satellites – they are not moons as they do not orbit Earth. For more information
Moon
Social science studying goods and services
(/ˌɛkəˈnɒmɪks, ˌiːkə-/) is a social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour
Economics
were forcibly imposed. The plains indigenous peoples mainly lived in stationary village sites surrounded by defensive walls of bamboo. The village sites
Taiwanese_indigenous_peoples
Event that is both extremely large in effect and of unique origins
that the statistical properties of the system are consistent over time (stationary), frequency and severity statistics may be constructed based on past observations
Dragon_king_theory
Periodic table of the elements with eight or more periods
Schiff, L. I.; Snyder, H.; Weinberg, J. (1940). "On the Existence of Stationary States of the Mesotron Field". Physical Review. 57 (4): 315–318. Bibcode:1940PhRv
Extended_periodic_table
Standard example in game theory
to be applied. One result of stochastic theory is that there exists a stationary vector v for the matrix v such that v ⋅ M = v {\displaystyle v\cdot M=v}
Prisoner's_dilemma
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QUASI STATIONARY-DISTRIBUTION
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