How to determine if a function is a correlation function of a process?

Asked Nov 10 '22 at 06:05

Active Nov 10 '22 at 06:05

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This page shows the corralation function of Wiener process X is $R(s,t)=\min (s,t)$.

I've learned how to compute the corralation function of a process, but now encountered an inverse problem: to determined if a function is a corralation function of some process.

The problem gives $f(s,t)=\min{(s,t)}$ as an example. Surely I know that it is a corralation function referring to the page mentioned, but what if I don't know (or cannot find) the original process? Is there and procedure to determine this?

asked Nov 10 '22 at 06:05

Nekomiya Kasane

Correlation functions are non-negative definite. – geetha290krm Nov 10 '22 at 06:09
Therefore if a function is non-negative definite, could I say that it must be a correlation function? – Nekomiya Kasane Nov 10 '22 at 06:13
See Theorem 1.2.3 in Ash and Gardner, Stochastic Processes. – geetha290krm Nov 10 '22 at 06:16
Thank you! I found it. – Nekomiya Kasane Nov 10 '22 at 06:28

How to determine if a function is a correlation function of a process?

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