The Wiener process at time $t=0$ is $0$.

It has independent increments, so $W_t-W_0 sim N(0,t-0)$, but wouldn't it mean that $W_tsim N(0,t)$ for every $t$?

But if I try to simulate a a Wiener-process in excel, it won't look like a Wiener process at all.

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#### Best Answer

@FelB you are not simulating a Wiener process because, tough $W_t sim N(0, t)$ they are not independent one from the other (If you simulate $N(0,t)$ independents. in n cells you won't get a WP).

What are independent are the increments.

In Excel, you could simulate n i.i.d $N(0,1)$ in a column, then compute the cumulative sum (i.e if in column A you have the simulated random variables, you set B1 = A1, and then B2 = B1 + A2, B3 = B2 + A3,…).

PLotting B is a fair approximation to a Wiener process and its quite standard.

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