Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and set (tau_{a}=inf left{s geqslant 0: B_{s}=aight}) where (a in

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$ and set $\tau_{a}=\inf \left\{s \geqslant 0: B_{s}=aight\}$ where $a \in \mathbb{R}$. Show that $\tau_{a} \sim \tau_{-a}$ and $\tau_{a} \sim a^{2} \tau_{1}$.

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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}) and set (tau_{a}=inf left{s geqslant 0: B_{s}=aight}) where (a in

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

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