Autocorrelation Function

[fenixtx423]

Hello all,

I am doing some work with random fields and I have found a variance reduction function (VRF) that fits my data perfectly. I would like to calculate the autocorrleation function (ACF) that goes with this variance reduction function. I have set the problem up using the definition that relates the VRF to the ACF, as shown in the photo below (c1 and c2 are fitting parameters for the VRF):

< link to objectionable page removed >

Is there a way to calculate the ACF funciton which is represented in the photo by f(x)? Normally I think most people go the other direction, and calculate the VRF from a known ACF.

Thanks so much in advance.

 

[Ishuda]

Hello all,

I am doing some work with random fields and I have found a variance reduction function (VRF) that fits my data perfectly. I would like to calculate the autocorrleation function (ACF) that goes with this variance reduction function. I have set the problem up using the definition that relates the VRF to the ACF, as shown in the photo below (c1 and c2 are fitting parameters for the VRF):

<link removed>

Is there a way to calculate the ACF funciton which is represented in the photo by f(x)? Normally I think most people go the other direction, and calculate the VRF from a known ACF.

Thanks so much in advance.

There is a theorem called the Fundamental Theorem of Calculus which might be of use. That is, if
\(\displaystyle g(x) = \int\limits_{0}^{x} h(x) dx\)
then, under certain conditions,
\(\displaystyle g'(x) = h(x)\)