Related papers: Moderate deviation and exit time estimates for sta…
The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the theory of max-stable processes of de Haan and…
We prove that the stationary measures for the free-energy increment process for the geometric last passage percolation (LPP) and log-gamma polymer model on a diagonal strip is given by a marginal of a two-layer Gibbs measure with a simple…
We prove a moderate deviation principle for the continuous time interpolation of discrete time recursive stochastic processes. The methods of proof are somewhat different from the corresponding large deviation result, and in particular the…
We consider finite element solutions to optimization problems, where the state depends on the possibly constrained control through a linear partial differential equation. Basing upon a reduced and rescaled optimality system, we derive a…
We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.
We consider a system of N particles with a stochastic dynamics introduced by Brunet and Derrida. The particles can be interpreted as last passage times in directed percolation on {1,...,N} of mean-field type. The particles remain grouped…
We formulate and solve the fixed horizon linear quadratic covariance steering problem in continuous time with a terminal cost measured in Hilbert-Schmidt (i.e., Frobenius) norm error between the desired and the controlled terminal…
We study the long-time behavior of a point mass moving in a one-dimensional viscous compressible fluid. Previously, we showed that the velocity of the point mass $V(t)$ satisfies a decay estimate $V(t)=O(t^{-3/2})$~[K. Koike, J.…
We study first passage percolation on the plane for a family of invariant, ergodic measures on $\mathbb{Z}^2$. We prove that for all of these models the asymptotic shape is the $\ell$-$1$ ball and that there are exactly four infinite…
We prove a refined version of the Aldous and Brown's exponential approximation of stationary hitting times. These are valid for all reversible Markov chains. We then specialise our estimates for vertex-transitive graphs, where we obtain…
This paper proposes a backstepping boundary control design for robust stabilization of linear first-order coupled hyperbolic partial differential equations (PDEs) with Markov-jumping parameters. The PDE system consists of 4 X 4 coupled…
The accurate estimation of scaling exponents is central in the observational study of scale-invariant phenomena. Natural systems unavoidably provide observations over restricted intervals; consequently a stationary stochastic process (time…
We show that the number of maximal paths in directed last-passage percolation on the hypercubic lattice ${\mathbb Z}^d$ $(d\geq2)$ in which weights take finitely many values is typically exponentially large.
We study deviation of U-statistics when samples have heavy-tailed distribution so the kernel of the U-statistic does not have bounded exponential moments at any positive point. We obtain an exponential upper bound for the tail of the…
For first passage percolation on $\mathbb{Z}^2$ with i.i.d. bounded edge weights, we consider the upper tail large deviation event; i.e., the rare situation where the first passage time between two points at distance $n$, is macroscopically…
The problem of optimal stopping with finite horizon in discrete time is considered in view of maximizing the expected gain. The algorithm proposed in this paper is completely nonparametric in the sense that it uses observed data from the…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
This paper studies quantitative deviation bounds for statistical ensembles evolving under the one-parameter flow of a nearly integrable Hamiltonian system. Combining Nekhoroshev-type stability estimates with phase-mixing arguments, we…
We consider a $\mathbb{R}^d$-valued branching random walk with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. With the help of the…
In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We…