An extension to the Wiener space of the arbitrary functions principle

Details An extension to the Wiener space of the arbitrary functions principle An extension to the Wiener space of the arbitrary functions principle

2006-10-17

arxiv.org/abs/math/0610509v1

Comptes rendus de l'acad\'{e}mie des sciences, Math\'{e}matiques 343 (2006) 329-332

Mathematics

Probability

Scientific paper

The arbitrary functions principle says that the fractional part of $nX$ converges stably to an independent random variable uniformly distributed on the unit interval, as soon as the random variable $X$ possesses a density or a characteristic function vanishing at infinity. We prove a similar property for random variables defined on the Wiener space when the stochastic measure $dB\_s$ is crumpled on itself.

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