 Independent coordinates of a compound Poisson process

ID: independent-coordinates-of-a-compound-poisson-process

The coordinates of a vector-valued Compound Poisson process are independent exactly when its Lévy measure is supported on the union of the coordinate axes. For marks

(g_{1} (U), g_{2} (U))

with

U

uniform on

[0, 1]

and continuous

g_{i}

, this is equivalent to

g_{1} (y) g_{2} (y) = 0

for every

y \in [0, 1]

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