Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}) and let (tau_{0}) be the first hitting time of 0

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}$ and let $\tau_{0}$ be the first hitting time of 0 . Find the "density" of $\mathbb{P}^{x}\left(B_{t} \in d z, \tau_{0}>tight)$, i.e. find the function $f_{t, x}(z)$ such that

\[\mathbb{P}^{X}\left(B_{t} \in A, \tau_{0}>tight)=\int_{A} f_{t, x}(z) d z \quad \text { for all } A \in \mathscr{B}(\mathbb{R})\]

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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}) and let (tau_{0}) be the first hitting time of 0

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

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