GaussâMarkov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary GaussâMarkov process is unique[ citation needed] up to rescaling; such a process is also known as an OrnsteinâUhlenbeck process.
GaussâMarkov processes obey Langevin equations. [3]
Every GaussâMarkov process X(t) possesses the three following properties: [4]
Property (3) means that every non-degenerate mean-square continuous GaussâMarkov process can be synthesized from the standard Wiener process (SWP).
A stationary GaussâMarkov process with variance and time constant has the following properties.
There are also some trivial exceptions to all of the above.[ clarification needed]
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cite book}}
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GaussâMarkov stochastic processes (named after Carl Friedrich Gauss and Andrey Markov) are stochastic processes that satisfy the requirements for both Gaussian processes and Markov processes. [1] [2] A stationary GaussâMarkov process is unique[ citation needed] up to rescaling; such a process is also known as an OrnsteinâUhlenbeck process.
GaussâMarkov processes obey Langevin equations. [3]
Every GaussâMarkov process X(t) possesses the three following properties: [4]
Property (3) means that every non-degenerate mean-square continuous GaussâMarkov process can be synthesized from the standard Wiener process (SWP).
A stationary GaussâMarkov process with variance and time constant has the following properties.
There are also some trivial exceptions to all of the above.[ clarification needed]
{{
cite book}}
: CS1 maint: multiple names: authors list (
link)