SuperGauss (version 1.0.2)

acf2msd: Convert autocorrelation of stationary increments to mean squared displacement of posititions.

Description

Converts the autocorrelation (ACF) of stationary increments to the mean squared displacement (MSD) of the corresponding positions.

Usage

acf2msd(acf)

Arguments

acf

length-N ACF vector of a stationary increment sequence.

Value

Length-N MSD vector of the corresponding positions.

Details

If \(X(t)\) is a stationary increments process, then \(\Delta X_0, \Delta X_1, \ldots\) with $$ \Delta X_n = X((n+1)\Delta t) - X(n \Delta t) $$ is a stationary time series. This function converts the ACF of this series into the MSD of the corresponding positions, namely returns the sequence \(\eta_1, \ldots, \eta_N\), where \(\eta_i = \mathrm{var}(X(i\Delta t))\).

Examples

# NOT RUN {
acf2msd(acf = exp(-(0:10)))
# }