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Every continuous first order autoregressive stochastic process is a Gaussian process. (English) Zbl 0784.60042

The notion of a process \(X(t)\) with independent increments is generalized. It is required that for \(0=t_ 0<t_ 1<\cdots<t_ n \leq T\) the r.v.s. \(X(t_ 0)\), \(X(t_ 1)-\alpha(t_ 0,t_ 1)X(t_ 0),\ldots,X(t_ n)-\alpha(t_{n-1},t_ n)X(t_{n-1})\) are independent with some suitable function \(\alpha(s,t)\). It is established that under some mild additional conditions every continuous process from this class is a Gauss-Markov process.

MSC:

60G15 Gaussian processes
60J99 Markov processes
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References:

[1] W. Feller: An Introduction to Probability Theory and 1ts Application. Vol. II. J. Wiley k Sons, New York 1971.
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