SDE valuation equation (stochastic calculus)

[cppIStough]

I read from a text: "suppose a stock with price $S$ and variance $v$ satisfies the SDE $$dS_t = u_tS_tdt+\sqrt{v_t}S_tdZ_1$$$$dv_t = \alpha dt+\eta\beta\sqrt{v_t}dZ_2$$ with $$\langle dZ_1 dZ_2\rangle = \rho dt$$ where $\mu_t$ is the drift of stock price returns, $\eta$ the volatility of volatility and $\rho$ the correlation between random stock price returns and changes in $v_t$. $dZ_1,dZ_2$ are Weiner processes.

I don't really understand the third equation. Can someone help me make sense? I understand quadratic variation, but I thought $dZ_1dZ_2 = 0$ unless 1=2, which then implies $dZ_1dZ_2 =dZ_1^2 = dt$; where does the $\rho$ come from, and I also don't understand the angled brackets (no definition from the text, is this supposed to be some inner product?)

 

[pasmith]

$\rho$ is stated to be the correlation between the processes; see e.g. here.

For the meaning of angle brackets, see here.