Given a stochastic differential equation:
$$ dx=a(x,t)dt+b(x,t)dW(t) $$
where $x$ is a random variable, $a(x,t)$ is a function of $x$ and $t$; called drift term, and $b(x,t)$ is the diffusion term. Brownian motion is $dW(t)$.
Is there a relationship between the time increment $dt$ and the time step for Brownian motion? In another way is it correct that: $$ \delta t=\sqrt dt $$ where $\delta t$ is Brownian motion time step.
In rough words, so you can confirm your intuition, if you were asked to simulate the process on a timegrid (a bunch of "dt"), you will simulate $dW_t$ using $dW_t=\sqrt{dt}Y$ where Y is normally distributed (mean 0, variance 1).