We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. First, we prove a large deviations result in the context of hashing with linear probing. By the way, we establish a large deviations result for triangu...
Due to their flexibility, Gaussian processes (GPs) have been widely used in nonparametric function estimation. A prior information about the underlying function is often available. For instance, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all inputs. We develop a finite-dimensio...
We consider an infinite chain of coupled harmonic oscillators with a Langevin thermostat attached at the origin and energy, momentum and volume conserving noise that models the collisions between atoms. The noise is rarefied in the limit, {that corresponds to the hypothesis} that in the macroscopic unit time only a finite number of collisions takes...
Let $x \mapsto x+ \alpha$ be a rotation on the circle and let $\varphi$ be a step function. We denote by $\varphi\_n (x)$ the corresponding ergodic sums $\sum\_{j=0}^{n-1} \varphi(x+j \alpha)$. Under an assumption on $\alpha$, for example when $\alpha$ has bounded partial quotients, and a Diophantine condition on the discontinuity points of $\varph...
In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expec...
This paper deals with the existence and the uniqueness of the solution to sweeping processes perturbed by a continuous signal of finite p-variation with $p\in [1,3[$. It covers pathwise stochastic multiplicative noises directed by a fractional Brownian motion of Hurst parameter greater than 1/3.
The behavior of the maximal displacement of a supercritical branching random walk has been a subject of intense studies for a long time. But only recently the case of time-inhomogeneous branching has gained focus. The contribution of this paper is to analyze a time-inhomogeneous model with two levels of randomness. In the first step a sequence of b...
Let µ = (µt)t∈R be any 1-parameter family of probability measures on R. Its quantile process (Gt)t∈R : ]0, 1[ → RR, given by Gt(α) = inf{x ∈ R : µt(]−∞, x]) > α}, is not Markov in general. We modify it to build the Markov process we call “Markov-quantile”.We first describe the discrete analogue: if (µn)n∈Z is a family of probability measures on R, a...
We investigate the effects of the propagation of a non-degenerate Brownian noise through a chain of deterministic differential equations whose coefficients are rough and satisfy a weak like H{\"o}rmander structure (i.e. a non-degeneracy condition w.r.t. the components which transmit the noise). In particular we characterize, through suitable counte...
For several decades, the no-arbitrage (NA) condition and the martingale measures have played a major role in the financial asset's pricing theory. Here, we propose a new approach based on convex duality instead of martingale measures duality : our prices will be expressed using Fenchel conjugate and bi-conjugate. This is lead naturally to a weak co...
