Given some random process that increments by independant gausian process Y, ie in time 2, X2=Y1+Y2: If i look at the process starting at some point not zero say at 4 ie X4 up to 7 then can:
P(X₄X₇>a) be written as: P(X₇>a/X₄)=P(Y₅+Y₆+Y₇>a/X₄) ie at the new starting point can X4 be taken as non random and just some number?