Abstract
Let X be a random variable in ℝp distributed symmetrically about zero with cumulants of order 4, 8, 12, … equal to zero. This class of random variables includes the multivariate normal. Consider the linear integral operator KX defined by
acting on the space of functions g: ℂp→ℂq with Taylor series expansions about zero. By Fredholm theory, non-degenerate integral operators in L2 generally do not have inverses. But KX is not in L2. We show that KX has inverse
, i=√−1.
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