# How can I simulate increments of a two dimensional brownian motion?

I am attempting to simulate an sde system of the following form $$dX_t=\sqrt{\vert aX+bY\vert}dW^1_t \\ dY_t=\sqrt{\vert cX+dY \vert}dW^2_t$$ where $$W=(W^1,W^2)$$ is a standard two dimensional Brownian motion by using the Euler scheme. $$X(t_{i+1})=X(t_i)+\sqrt{\vert aX(t_i)+bY(t_i)\vert} (W^{(1)}(t_{i+1})-W^{(1)}(t_i))\\ Y(t_{i+1})=Y(t_i)+\sqrt{\vert cX(t_i)+dY(t_i)\vert} (W^{(2)}(t_{i+1})-W^{(2)}(t_i))$$

. In order to implement an euler scheme in Java I intend to use a Standard normal sample generator from

My question is that every time step of the Euler-Maruyama scheme can i just use normal distribution with variance $$t_{i+1}-t_i$$ to sample both $$(W^{(1)}(t_{i+1})-W^{(1)}(t_i))$$ and $$(W^{(2)}(t_{i+1})-W^{(2)}(t_i))$$.