Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a one-dimensional Brownian motion. Which of the following processes are martingales?
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Let \(\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}\) be a one-dimensional Brownian motion. Which of the following processes are martingales?
a) \(U_{t}=e^{c B_{t}}, c \in \mathbb{R}\);
b) \(V_{t}=t B_{t}-\int_{0}^{t} B_{s} d s\);
c) \(W_{t}=B_{t}^{3}-t B_{t}\);
d) \(X_{t}=B_{t}^{3}-3 \int_{0}^{t} B_{s} d s\);
e) \(Y_{t}=\frac{1}{3} B_{t}^{3}-t B_{t}\)
f) \(Z_{t}=e^{B_{t}-c t}, c \in \mathbb{R}\).
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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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