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12 papers · 2 filters
Asymptotic independence of multiple Wiener-Itô integrals and the resulting limit laws
Ivan Nourdin, Jan Rosiński
We characterize the asymptotic independence between blocks consisting of multiple Wiener-Itô integrals. As a consequence of this characterization, we derive the celebrated fourth m…
Hitting time for Bessel processes - walk on moving spheres algorithm (WoMS)
Madalina Deaconu, Samuel Herrmann
In this article we investigate the hitting time of some given boundaries for Bessel processes. The main motivation comes from mathematical finance when dealing with volatility mode…
Central and non-central limit theorems in a free probability setting
Ivan Nourdin, Murad Taqqu
Long-range dependence in time series may yield non-central limit theorems. We show that there are analogous time series in free probability with limits represented by multiple Wign…
Optimal Berry-Esseen rates on the Wiener space: the barrier of third and fourth cumulants
Hermine Biermé, Aline Bonami, Ivan Nourdin +1
Let {F_n} be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E[F_n^4] --> E[N^4]=3, where N is a stan…
Bacterial persistence: a winning strategy?
Olivier Garet, Regine Marchand, Rinaldo B. Schinazi
It has long been known that antibiotic treatment will not completely kill off a bacteria population. For many species a small fraction of bacteria is not sensitive to antibiotics.…
Splitting trees with neutral Poissonian mutations II: Largest and Oldest families
Nicolas Champagnat, Amaury Lambert
We consider a supercritical branching population, where individuals have i.i.d. lifetime durations (which are not necessarily exponentially distributed) and give birth (singly) at…