Hello math stack exchange! Suppose we have arbitrary function of stochastic processes $X_i(t)$, like $$Y(t) = X_1(t) + X_2(t) - X_3(t) + X_4(t) ....,$$ more generally $Y(t) = f(X_1(t), X_2(t), X_3(t)...).$
Is there a general theory of detecting the "presence" of certain process $X_a(t)$ by observing only $Y(t)$? Each process $X_i(t)$ are not noise but behave similarly with different parameters, doesn't change much in short term, possibly stationary. $X_a(t)$ changes very abruptly and I want to detect the presence of $X_a(t)$ in $Y(t)$.
This might be somewhat related to bayesian inference stuffs but I'm not fully sure where to start looking at. Even random throwing of keywords would be helpful thanks!