Let (B_{t}=left(b_{t}, beta_{t}ight), t geqslant 0), be a two-dimensional Brownian motion. a) Show that (W_{t}:=frac{1}{sqrt{2}}left(b_{t}+beta_{t}ight)) is a

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Let $B_{t}=\left(b_{t}, \beta_{t}ight), t \geqslant 0$, be a two-dimensional Brownian motion.

a) Show that $W_{t}:=\frac{1}{\sqrt{2}}\left(b_{t}+\beta_{t}ight)$ is a $\mathrm{BM}^{1}$.

b) Are $X_{t}:=\left(W_{t}, \beta_{t}ight)$ and $Y_{t}:=\frac{1}{\sqrt{2}}\left(b_{t}+\beta_{t}, b_{t}-\beta_{t}ight), t \geqslant 0$, two-dimensional Brownian motions?

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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 (B_{t}=left(b_{t}, beta_{t}ight), t geqslant 0), be a two-dimensional Brownian motion. a) Show that (W_{t}:=frac{1}{sqrt{2}}left(b_{t}+beta_{t}ight)) is a

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

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