Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (X_{t}=exp left(a B_{t}+b tight), t geqslant 0),

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Let $\left(B_{t}, \mathscr{F}_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Show that $X_{t}=\exp \left(a B_{t}+b tight), t \geqslant 0$, is a martingale if, and only if, $a^{2} / 2+b=0$.

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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 17, 2024 01:00 AM

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Let (left(B_{t}, mathscr{F}_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (X_{t}=exp left(a B_{t}+b tight), t geqslant 0),

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

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