On the decomposition of continuous flows on the Polish space
On the existence of uniformly distributed sequences in compact spaces
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably...
On the spectral norm of a random Toeplitz matrix.
On the stability of interacting processes with applications to filtering and genetic algorithms
On the Urysohn condition and the convergence of probability distributions
On uniform tail expansions of multivariate copulas and wide convergence of measures
The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of...
On weak convergence of filtrations
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On weak solutions of random differential inclusions.
Operator-stable probability measures on Banach spaces
Penalisation of a stable Lévy process involving its one-sided supremum
Penalisation involving the one-sided supremum for a stable Lévy process with index α∈(0, 2] is studied. We introduce the analogue of Azéma–Yor martingales for a stable Lévy process and give the law of the overall supremum under the penalised measure.
Pénalisations de l’araignée brownienne
Dans cet article, nous pénalisons la loi d’une araignée brownienne prenant ses valeurs dans un ensemble fini de demi-droites concourantes, avec un poids égal à , où est un réel positif, une famille de réels indexés par , un paramètre réel, la distance de à l’origine, () la demi-droite sur laquelle se trouve , le temps local de à l’origine, et la constante de normalisation. Nous montrons que la famille des mesures de probabilité obtenue par ces pénalisations converge vers...
Periodic and almost periodic flows of periodic Ito equations
Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the -bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.
Prämessbare Funktionen.
Probabilities on contractible locally compact groups : the existence of universal distributions in the sense of W. Doeblin
Product of exponentials and spectral radius of random k-circulants
We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...
Produits scalaires sur l'espace des mesures
Proof(s) of the Lamperti representation of continuous-state branching processes.
Propagation of chaos for Burgers' equation