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In the following paper, what does the symbol $\Phi$ in equation $3.1$ (page $3$) represent? Does it represent the normal distribution?

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I am new to brownian motion but it seems to be related to this topic. Sorry if this question is vague. – user1234440 May 14 '13 at 18:35
up vote 3 down vote accepted

$\Phi(x)$ typically (and which is what is also means in the article you have linked to) represents a suitably normalized error function, equivalently the cummulative distribution function of the normal distribution, i.e., $$\Phi(x) = \dfrac1{\sqrt{2 \pi}}\int_{-\infty}^{x} \exp(-t^2/2)dt$$

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so in the PDF, the variables inside the phi symbol represents a point on the CDF correct? So phi(0) should equal 0.5? – user1234440 May 14 '13 at 18:41
@user1234440 Yes. $\Phi(0) = 0.5$. I got confused with your use of PDF (probability density function/ portable document format) :-). – user17762 May 14 '13 at 18:43
Sorry! I am trying to code up in R the expected drawdown equation E(D), but am not getting results similar to the graph shown in the next page. – user1234440 May 14 '13 at 18:45

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