English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let T be a measurable transformation of a probability space $(E,\mathcal{E},\pi)$, preserving the measure {\pi}. Let X be a random variable with law\pi. Call K(\cdot, \cdot) a regular version of the conditional law of X givenT(X). Fix $B\in \mathcal {E}$. We first prove that if B is reachable from\pi-almost every point for a Markov chain of kernel K, then the T-orbit of\pi-almost every point X visits B. We then apply this result to the L\'evytransform, which transforms the Brownian motion W into the Brownian motion |W|- L, where L is the local time at 0 of W. This allows us to get a new proof ofMalric's theorem which states that the orbit under the L\'evy transform ofalmost every path is dense in the Wiener space for the topology of uniformconvergence on compact sets.

Densit\'e des orbites des trajectoires browniennes sous l'action de la transformation de L\'evy