What is the popular way to simulate an Ito process?

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Ito formula is defined as a process of the form

$$ X(t)=X(0)+\int_0^t\delta(s)dW_s +\int_0^t\theta(s)ds $$

one obvious way to simulate it is to first generate a Brownian motion and then use the Euler method.

But are there better ways?