Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (mathbb{P}left(sup _{s leqslant t}left|B_{s}ight| geqslant xight) leqslant 2

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$. Show that $\mathbb{P}\left(\sup _{s \leqslant t}\left|B_{s}ight| \geqslant xight) \leqslant 2 \mathbb{P}\left(\left|B_{t}ight| \geqslant xight), x, t \geqslant 0$.

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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 17, 2024 01:00 AM

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Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}). Show that (mathbb{P}left(sup _{s leqslant t}left|B_{s}ight| geqslant xight) leqslant 2

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

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