For the stochastic equation studied in the text, show that [overline{X(t)^{2}}=frac{sigma^{2}}{alpha^{2}}left(t+frac{1}{2 alpha} e^{-2 alpha t} ight)

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For the stochastic equation studied in the text, show that

\[\overline{X(t)^{2}}=\frac{\sigma^{2}}{\alpha^{2}}\left(t+\frac{1}{2 \alpha} e^{-2 \alpha t}\right) \rightarrow \frac{\sigma^{2}}{\alpha^{2}} t\]

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