Noise with linear trends

First we consider the simplest case: correlated noise with a linear trend. A linear trend

$$u(i)=A_{\rm L} i$$ (5)

is characterized by only one variable -- the slope of the trend, $A_{\rm L}$. For convenience, we denote the rms fluctuation function for noise without trends by $F_{\rm\eta }(n)$, linear trends by $F_{\rm L}(n)$, and noise with a linear trend by $F_{\rm\eta L}(n)$.