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]

[itex]\rho[/itex] is stated to be the correlation between the processes; see e.g. here.

For the meaning of angle brackets, see here.