Let (left(B_{t}ight)_{t in mathbb{R}_{+}})denote a standard Brownian motion. Compute the stochastic integrals [ int_{0}^{T} 2 d B_{t}

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Let $\left(B_{t}ight)_{t \in \mathbb{R}_{+}}$denote a standard Brownian motion. Compute the stochastic integrals

\[ \int_{0}^{T} 2 d B_{t} \quad \text { and } \quad \int_{0}^{T}\left(2 \times \mathbb{1}_{[0, T / 2]}(t)+\mathbb{1}_{(T / 2, T]}(t)ight) d B_{t} \]

and determine their probability distributions (including mean and variance).

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Introduction To Stochastic Finance With Market Examples

ISBN: 9781032288277

2nd Edition

Authors: Nicolas Privault

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Question Posted: Feb 25, 2024 08:00 AM

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Let (left(B_{t}ight)_{t in mathbb{R}_{+}})denote a standard Brownian motion. Compute the stochastic integrals [ int_{0}^{T} 2 d B_{t}

Question:

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By Definition 45 we have int0T 2 d Bt2leftBTB0ight2 BT which has a Gaussian distribution ...View the full answer

Introduction To Stochastic Finance With Market Examples

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