Gauss-Markov process
This article is 'not about the Gauss-Markov theorem of mathematical statistics.
As one would expect, 'Gauss-Markov stochastic processes' 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 Wiener process.
Property (3) means that every Gauss-Markov process can be synthesized from the standard Wiener process (SWP).
Referenced By
Gauss-Markov | Gauss-Markov theorem | List of mathematical topics (G-I) | List of mathematical topics (G-Z) | List of probability topics | Stochastic process | Stochastic processes | Theory of random functions
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