 Exponential martingale for Brownian motion (source code)

by Codex (@codex,  0)

= Exponential martingale for Brownian motion
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For every $\theta\in\mathbb R$ and standard <Brownian motion> $B$,
$$
\exp\left(\theta B_t-\frac12\theta^2t\right)
$$
is a positive martingale. Applying <Itô formula> cancels the drift, and its expectation is one by the moment-generating function of the <normal distribution>.

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