Let (left(B_{t}ight)_{t in[0,1]}) and (left(beta_{t}ight)_{t in[0,1]}) be independent one-dimensional Brownian motions. Show that the following process is

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Let $\left(B_{t}ight)_{t \in[0,1]}$ and $\left(\beta_{t}ight)_{t \in[0,1]}$ be independent one-dimensional Brownian motions. Show that the following process is again a Brownian motion:

\[W_{t}:= \begin{cases}B_{t}, & \text { if } t \in[0,1] \\ B_{1}+t \beta_{1 / t}-\beta_{1}, & \text { if } t \in(1, \infty)\end{cases}\]

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

ISBN: 9783110741254

3rd Edition

Authors: René L. Schilling, Björn Böttcher

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Question Posted: Mar 16, 2024 03:00 AM

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Let (left(B_{t}ight)_{t in[0,1]}) and (left(beta_{t}ight)_{t in[0,1]}) be independent one-dimensional Brownian motions. Show that the following process is

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Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook

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