For a finite measure Λ on [0, 1], the Λ-coalescent is a coalescent process such that, whenever there are b clusters, each k-tuple of clusters merges into one at rate ∫01xk−2(1−x)b−kΛ(dx). It has recently been shown that if 1<α<2, the Λ-coalescent in which Λ is the Beta (2−α, α) distribution can be used to describe the genealogy of a continuous-state branching process (CSBP) with an α-stable branching mechanism. Here we use facts about CSBPs to establish new results about the small-time...

The aim of this paper is to study the threshold behavior for the satisfiability property of a random $k$-XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with $k$ variables per equation. For $k\ge 3$ we show the existence of a sharp threshold for the satisfiability of a random $k$-XOR-CNF formula, whereas there are smooth thresholds for $k=1$ and $k=2$.

The aim of this paper is to study the threshold behavior for the satisfiability property of a random k-XOR-CNF formula or equivalently for the consistency of a random Boolean linear system with k variables per equation. For k ≥ 3 we show the existence of a sharp threshold for the satisfiability of a random k-XOR-CNF formula, whereas there are smooth thresholds for k=1 and k=2.

This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the smoothed paths. Various classes of stochastic processes are considered starting with the Wiener process,...

Let $B^{H_i,K_i}=\{B_t^{H_i,K_i},t\ge 0\}$, $i=1,2$ be two independent, $d$-dimensional bifractional Brownian motions with respective indices $H_i\in (0,1)$ and $K_i\in (0,1]$. Assume $d\ge 2$. One of the main motivations of this paper is to investigate smoothness of the collision local time $${\ell }_T={\int }_0^T\delta (B_s^{H_1,K_1}-B_s^{H_2,K_2})\mathrm{d}s,T>0,$$ where $\delta$ denotes the Dirac delta function. By an elementary method we show that ${\ell }_T$ is smooth in the sense of Meyer-Watanabe if and only if $min\{H_1{K}_1,H_2{K}_2\}<1/(d+2)$.

The transition kernel of the well-known Metropolis-Hastings (MH) algorithm has a point mass at the chain’s current position, which prevent direct smoothness properties to be derived for the successive densities of marginals issued from this algorithm. We show here that under mild smoothness assumption on the MH algorithm “input” densities (the initial, proposal and target distributions), propagation of a Lipschitz condition for the iterative densities can be proved. This allows us to build a consistent...

We give a characterization of those probability measures on the real line which satisfy certain Sobolev inequalities. Our starting point is a simpler approach to the Bobkov-Götze characterization of measures satisfying a logarithmic Sobolev inequality. As an application of the criterion we present a soft proof of the Latała-Oleszkiewicz inequality for exponential measures, and describe the measures on the line which have the same property. New concentration inequalities for product measures follow....

In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means...

Se considera una solución recursiva para una cadena de Markov n-dimensional en tiempo continuo, basada en una función entera K y en la que aparece una familia de polinomios. Se hace un estudio de esta familia, a partir del análisis de una clase de subconjuntos de Im(K), con el objetivo de encontrar la subfamilia de polinomios que aparece explícitamente en la solución recursiva, en términos de la distribución de probabilidad absoluta de la cadena, y la subfamilia que es necesario y suficiente calcular...