Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Decide which of the following processes are Brownian motions: a)

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Decide which of the following processes are Brownian motions:

a) $X_{t}:=2 B_{t / 4}$;

b) $Y_{t}:=B_{2 t}-B_{t}$;

c) $Z_{t}:=\sqrt{t} B_{1}$

$(t \geqslant 0)$.

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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 geqslant 0}) be a (mathrm{BM}^{1}). Decide which of the following processes are Brownian motions: a)

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We can analyze each process to see if it satisfies the properties of a Brownian motion BM Properties of a Brownian Motion BM B0 0 starts at zero Indep...View the full answer

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

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