We consider a branching Brownian motion in $\mathbb{R}^d$. We prove that there exists a random subset $\Theta$ of $\mathbb{S}^{d-1}$ such that the limit of the derivative martingale exists simultaneously for all directions $\theta \in \Theta$ almost surely. This allows us to define a random measure on $\mathbb{S}^{d-1}$ whose density is given by th...
We provide an exhaustive treatment of Linear-Quadratic control problems for a class of stochastic Volterra equations of convolution type, whose kernels are Laplace transforms of certain signed matrix measures which are not necessarily finite. These equations are in general neither Markovian nor semimartingales, and include the fractional Brownian m...
This paper is devoted to the uncertainty quantification for 3D acoustic performance model of nacelle liners (acoustic treatments). Uncertainties are taken into account in order to increase the robustness of the predictions. A full computational acoustic propagation model based on the convected Helmholtz equation in presence of a non-homogeneous flo...
In the regression model $Y = b(X) +\varepsilon$, where $X$ has a density $f$, this paper deals with an oracle inequality for an estimator of $bf$, involving a kernel in the sense of Lerasle et al. (2016), selected via the PCO method. In addition to the bandwidth selection for kernel-based estimators already studied in Lacour, Massart and Rivoirard ...
We are interested in recovering information on a stochastic block model from the subgraph discovered by an exploring random walk. Stochastic block models correspond to populations structured into a finite number of types, where two individuals are connected by an edge independently from the other pairs and with a probability depending on their type...
We consider the Riemannian random wave model of Gaussian linear combinations of Laplace eigenfunctions on a general compact Riemannian manifold. With probability one with respect to the Gaussian coefficients, we establish that, both for large band and monochro-matic models, the process properly rescaled and evaluated at an independently and uniform...
This paper studies the limit of a kinetic evolution equation involving a small parameter and driven by a random process which also scales with thesmall parameter. In order to prove the convergence in distribution to the solution of a stochastic diffusion equation while removing a boundedness assumption on the driving random process, we adapt the me...
Liouville conformal field theory (denoted LCFT) is a 2-dimensional conformal field theory depending on a parameter γ ∈ R and studied since the eighties in theoretical physics. In the case of the theory on the 2-sphere, physicists proposed closed formulae for the n-point correlation functions using symmetries and representation theory, called the DO...
We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Hölder continuity assumptions on the drift. Importantly, the estimates re...
The goal of the current paper is to provide the basins of attraction of the granular media equation when there are exactly three stable states. Indeed, it has been proved in our previous works [18, 19] that there is convergence. However, very few is known about the basins of attraction. We provide them with a small diffusion coefficient. The techni...
