A counter-example to the Cantelli conjecture

Details A counter-example to the Cantelli conjecture A counter-example to the Cantelli conjecture

2012-02-10

arxiv.org/abs/1202.2250v1

Mathematics

Probability

Scientific paper

In this paper, we construct a counter-example to a question by Cantelli, asking whether there exists a non-constant positive measurable function $\varphi$ such that for i.i.d. r.v. $X,Y$ of law N(0,1), the r.v. $X + f(X) Y$ is also Gaussian. For the construction that we propose, we introduce a new tool, the Brownian mass transport: the mass is transported by Brownian particles that are stopped in a specific way. This transport seems to be interesting by itself, turning out to be related to the Skorokhod and Stefan problems.

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