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