I have a simple question about the intuition behind property 1 of a Wiener Process. It says in my textbook that the change in a variable z that follows a Wiener Process is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]δz=ε\sqrt{δt}[/tex]

where ε is a random drawing from a [tex]\Phi(0,1)[/tex]

Now I think [tex]\sqrt{δt}[/tex] is supposed to be the standard deviation of a random variable which follows a normal distribution with a standard deviation of 1 during one year.

My question now is, if δ^1/2 is the standard deviation of a normally distributed random variable, why is the random drawing from another normal distribution necessary or basically why do I have to multiply ε with δt^1/2?

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# Wiener Process Properties

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