Let (B_{t}=left(b_{t}, beta_{t}ight), t geqslant 0), be a two-dimensional Brownian motion and (alpha in[0,2 pi)). Show that
Question:
Let \(B_{t}=\left(b_{t}, \beta_{t}ight), t \geqslant 0\), be a two-dimensional Brownian motion and \(\alpha \in[0,2 \pi)\). Show that \(W_{t}=\left(b_{t} \cdot \cos \alpha+\beta_{t} \cdot \sin \alpha, \beta_{t} \cdot \cos \alpha-b_{t} \cdot \sin \alphaight)^{\top}\) is a two-dimensional Brownian motion. Find a suitable \(d\)-dimensional generalization of this observation.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Brownian Motion A Guide To Random Processes And Stochastic Calculus De Gruyter Textbook
ISBN: 9783110741254
3rd Edition
Authors: René L. Schilling, Björn Böttcher
Question Posted: