I found a paper about the Black Scholes Merton Modell. In this paper it is claimed that $\Delta S_i$ is of order $O(\Delta t^{1/2})$.
I was able to determine $\Delta S_i$ out of $\frac{dS_i}{S_i}=\mu_idt+\beta_idz_0+\sigma_idz_i$. The result is $\frac{\Delta S_i}{S_i}=\exp\big((\beta_i z_0+\sigma_i z_i)\Delta t^{1/2}+(\mu_i-\frac{1}{2}\tilde{\sigma}_i^2)\Delta t\big)-1$
How can I show from there that $\Delta S_i$ is of order $O(\Delta t^{1/2})$?
I would be grateful for any help. Thanks in advance.
