I try to derive the expected value of $ E[S(t)X(t)] $ where S(t) is a Gaussian random process with mean M(t) and variance V(t), X(t) is a doubly stochastic Poisson process(DSPP) with intensity $$ \lambda (t) = KS(t) $$ where K is a constant. I derived the mean and variance for both of the processes. But it is a little bit hard to derive mean of their products since they are dependent. How can I start? Any book or paper will be appreciated.
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