Graduate SDE valuation equation (stochastic calculus)

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The discussion centers on the stochastic differential equation (SDE) for stock price modeling, specifically addressing the third equation involving the correlation between two Wiener processes, dZ1 and dZ2. The user expresses confusion about the correlation term ρ and the notation with angled brackets, questioning the assumption that dZ1dZ2 equals zero unless the indices are the same. Clarification is provided that ρ represents the correlation between the two stochastic processes, which is a key aspect of modeling their joint behavior. The angled brackets denote the expected value of the product of the differentials, which is a common notation in stochastic calculus. Understanding these concepts is crucial for accurately interpreting the dynamics of the stock price and its volatility.
cppIStough
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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?)
 
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\rho is stated to be the correlation between the processes; see e.g. here.

For the meaning of angle brackets, see here.
 
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