Let ({bar{B}(t), 0 leq t leq 1}) be the Brownian bridge. Prove that the stochastic process [{S(t),

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Let \(\{\bar{B}(t), 0 \leq t \leq 1\}\) be the Brownian bridge. Prove that the stochastic process

\[\{S(t), t \geq 0\} \text { defined by } S(t)=(t+1) \bar{B}\left(\frac{t}{t+1}\right)\]

is the standard Brownian motion.

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