- Gauss–Markov process
:"This article is not about the
Gauss–Markov theoremof mathematical statistics."
Gauss–Markov stochastic processes (named after
Carl Friedrich Gaussand Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes.
Every Gauss-Markov process "X"("t") possesses the three following properties:
# If "h"("t") is a non-zero scalar function of "t", then "Z"("t") = "h"("t")"X"("t") is also a Gauss-Markov process
# If "f"("t") is a non-decreasing scalar function of "t", then "Z"("t") = "X"("f"("t")) is also a Gauss-Markov process
# There exists a non-zero scalar function "h"("t") and a non-decreasing scalar function "f"("t") such that "X"("t") = "h"("t")"W"("f"("t")), where "W"("t") is the standard
Property (3) means that every Gauss–Markov process can be synthesized from the standard Wiener process (SWP).
A stationary Gauss–Markov process with
varianceand time constanthave the following properties.
The above yields the following spectral factorisation:
Wikimedia Foundation. 2010.
Look at other dictionaries:
Gauss–Markov theorem — This article is not about Gauss–Markov processes. In statistics, the Gauss–Markov theorem, named after Carl Friedrich Gauss and Andrey Markov, states that in a linear model in which the errors have expectation zero and are uncorrelated and have… … Wikipedia
Gauss–Markov — The phrase Gauss–Markov is used in two different ways. See *Gauss–Markov processes in probability theory. *The Gauss–Markov theorem in mathematical statistics (In this theorem, one does not assume the probability distributions are Gaussian.) … Wikipedia
Andrey Markov — For other people named Andrey Markov, see Andrey Markov (disambiguation). Andrey (Andrei) Andreyevich Markov Born June 14, 1856( … Wikipedia
List of topics named after Carl Friedrich Gauss — Carl Friedrich Gauss (1777 ndash; 1855) is the eponym of all of the topics listed below. Topics including Gauss *Carl Friedrich Gauss Prize, a mathematics award *Degaussing, to demagnetize an object *Gauss (unit), a unit of magnetic field (B)… … Wikipedia
Carl Friedrich Gauss — Infobox Scientist box width = 300px name = Carl Friedrich Gauss caption = Johann Carl Friedrich Gauss (1777 1855), painted by Christian Albrecht Jensen birth date = birth date|1777|4|30|df=y birth place = Braunschweig, Electorate of Brunswick… … Wikipedia
List of mathematics articles (G) — NOTOC G G₂ G delta space G networks Gδ set G structure G test G127 G2 manifold G2 structure Gabor atom Gabor filter Gabor transform Gabor Wigner transform Gabow s algorithm Gabriel graph Gabriel s Horn Gain graph Gain group Galerkin method… … Wikipedia
List of stochastic processes topics — In the mathematics of probability, a stochastic process can be thought of as a random function. In practical applications, the domain over which the function is defined is a time interval ( time series ) or a region of space ( random field… … Wikipedia
List of probability topics — This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.General aspects*Probability *Randomness, Pseudorandomness,… … Wikipedia
Maximum entropy spectral estimation — The maximum entropy method applied to spectral density estimation. The overall idea is that the maximum entropy rate stochastic process that satisfies the given constant autocorrelation and variance constraints, is a linear Gauss Markov process… … Wikipedia
Timeline of thermodynamics, statistical mechanics, and random processes — A timeline of events related to thermodynamics, statistical mechanics, and random processes. Ancient times *c. 3000 BC The ancients viewed heat as that related to fire. The ancient Egyptians viewed heat as related to origin mythologies. One… … Wikipedia