Let (left(B_{t}ight)_{t geqslant 0}) be a (mathrm{BM}^{1}, alpha>0) and consider the stochastic process (X_{t}:=e^{-alpha t / 2}

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Let $\left(B_{t}ight)_{t \geqslant 0}$ be a $\mathrm{BM}^{1}, \alpha>0$ and consider the stochastic process $X_{t}:=e^{-\alpha t / 2} B_{e^{\alpha t}}, t \geqslant 0$.

a) Determine $m(t)=\mathbb{E} X_{t}$ and $C(s, t)=\mathbb{E}\left(X_{s} X_{t}ight), s, t \geqslant 0$.

b) Find the probability density of $\left(X_{t_{1}}, \ldots, X_{t_{n}}ight)$ where \(0 \leqslant t_{1}<\cdots

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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}, alpha>0) and consider the stochastic process (X_{t}:=e^{-alpha t / 2}

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

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