When I'm reading "An Introduction to SPDE" by John B. Walsh, I met some problems in the chapter about Stochastic Integrals.
In Page 290, the author defined the covariance measure $$Q(A,B,(s,t])=<M(A),M(B)>_t-<M(A),M(B)>_s$$ , where M(A), M(B) are all martingales but may not be independent (because it didn't require that $M_t(A)$ is orthogonal martingale measure). Then, he gets the conclusion that $$\sum_{i=1}^{n}\sum_{j=1}^n a_ia_jQ(A_i,A_j,(s,t]) \ge 0$$ It involves the calculation of covariation process, but I don't know how to get this conclusion.
In Page 294, when he proves Lemma 2.4, he seems to use the conclusion that if $X,Y$ are martingales, then $$(X_t-X_s)(Y_t-Y_s)-(<X,Y>_t-<X,Y>_s)$$ which is also confusing me.
Can anyone give some related conclusions of covariation?