# Variance of integrated dynamical system

Define time increment $$\mu:=t_{k+1}-t_{k}$$. Consider the signal $$x(\mu)-\mathbb{E}[x(\mu)]$$ defined as

$$x(\mu)-\mathbb{E}[x(\mu)]=\frac{1}{\mu}\int_{t_{k}}^{t_{k+1}}\int_{0}^{\tau}e^{A(\tau-\delta)}G_{c}w(\delta) d \delta d\tau$$

where $$A_{c}$$, $$G_{c}$$ are constant matrices and $$w(\delta)$$~$$N(0,Q_{c})$$.

What is the variance of $$x(\mu)-\mathbb{E}[x(\mu)]$$?