Question: Define a weakly stationary stochastic process ({V(t), t geq 0}) by [V(t)=S(t+1)-S(t)] where ({S(t), t geq 0}) is the standard Brownian motion process. Prove that

Define a weakly stationary stochastic process \(\{V(t), t \geq 0\}\) by

\[V(t)=S(t+1)-S(t)\]

where \(\{S(t), t \geq 0\}\) is the standard Brownian motion process.

Prove that its spectral density is proportional to

\[\frac{1-\cos \omega}{\omega^{2}}\]

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