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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? 

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