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i need to perform the convolution of two normal vibariate. I defined

a = {Subscript[\[Sigma], 11], Subscript[\[Sigma], 21]}
b = {Subscript[\[Sigma], 12], Subscript[\[Sigma], 22]}
B1=PDF[BinormalDistribution[{0, 0}, a, Subscript[\[Rho], 1]], {x, y}]
B2=PDF[BinormalDistribution[{0, 0}, b, Subscript[\[Rho], 1]], {x, y}]

Could you please help me to move forward ? I tried to understand how to perform a 2D convolution in mathematica, without much success.

Thank you, Andrea

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No need to resort to numerical convolution for this classic problem. In 1D:

Convolve[
 PDF[NormalDistribution[m1, s1], x], 
 PDF[NormalDistribution[m2, s2], y], 
 x, y]

and likewise in 2D.

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sorry i think i found the answer

A[x, y] = 
  PDF[BinormalDistribution[{0, 0}, a, Subscript[\[Rho], 1]], {x, y}];
B[x, y] = 
  PDF[BinormalDistribution[{0, 0}, a, Subscript[\[Rho], 2]], {x, y}];
test[t, z] = N[Convolve[A[x, y], B[x, y], {x, y}, {t, z}]]

Best regards, Andrea

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