What is $dW^a_t dW^b_t$ for two various Wiener processes?

Question

I need to simplify $dW^a_t dW^b_t$ where $W^a_t$ and $W^b_t$ are two different Wiener processes. If I had only one process $W_t$, I could use the following properties:

$$ (dt)^2 = 0 \\ dt \text{ } dW_t = 0 \\ (dW_t)^2 = dt$$

Is it possible to do something similar with $dW^a_t dW^b_t$

Answer 1

Well, you can't have anything. But like, if you have the independence of two processes, the product is necessarily zero.