Gauss–Markov process

related topics
{math, number, function}
{acid, form, water}
{rate, high, increase}

Gauss–Markov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. The stationary Gauss–Markov process is a very special case because it is unique, except for some trivial exceptions.

Every Gauss–Markov process X(t) possesses the three following properties:

Property (3) means that every Gauss–Markov process can be synthesized from the standard Wiener process (SWP).

Properties of the Stationary Gauss-Markov Processes

A stationary Gauss–Markov process with variance \textbf{E}(X^{2}(t)) = \sigma^{2} and time constant β − 1 has the following properties.

Exponential autocorrelation:

A power spectral density (PSD) function that has the same shape as the Cauchy distribution:

(Note that the Cauchy distribution and this spectrum differ by scale factors.)

The above yields the following spectral factorization:

which is important in Wiener filtering and other areas.

There are also some trivial exceptions to all of the above.

Full article ▸

related documents
Wilhelm Ackermann
Super-Poulet number
Vladimir Voevodsky
Inductive logic programming
Mathematical constants (sorted by continued fraction representation)
Classical logic
Cypherpunk anonymous remailer
Tomaž Pisanski
Code word
Euler's sum of powers conjecture
Liouville function
Unix billennium
Ninety-ninety rule
FIPS county code
Type 1 encryption
Facade pattern
August Ferdinand Möbius
Structure and Interpretation of Computer Programs
Hill system
Wikipedia:Free On-line Dictionary of Computing/X - Z
Object-oriented programming language
National Center for Biotechnology Information
Shotgun debugging
Mrs. Miniver's problem
International Air Transport Association airport code