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})

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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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Applied Probability And Stochastic Processes

ISBN: 9780367658496

2nd Edition

Authors: Frank Beichelt

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Question Posted: Apr 26, 2024 04:01 PM

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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})

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Applied Probability And Stochastic Processes

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