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I encounterred a question on Stochastic Calculus as following, but I don't understand the meaning of $\mathcal{N}$ here, can any expert explain it?

$\mathbb{E}[\mathcal{N}(W_t)]=?$ where $W_t$ is standard Brownian Motion.

A follow-up is $\mathbb{E}[\mathcal{N}(W_t+a)]=?$ I was also blocked by the meaning of $\mathcal{N}$.

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    I don't know what is $\mathscr N$, could you put a source for this problem?2012-05-26
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    Hi Ilya, I am also not sure about it, it seems it's understandable to many stochastic analysis experts but I am not.2012-05-27
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    Hi Ilya, I know how to handle it, $\mathcal{N}$ is just the cdf of standard normal distribution.2012-06-02
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    Good. FYI, it is usually denoted through $\Phi$2012-06-02

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