Related papers: Integrability of solutions of the Skorokhod Embedd…
We present some new results on sample path optimality for the ergodic control problem of a class of non-degenerate diffusions controlled through the drift. The hypothesis most often used in the literature to ensure the existence of an a.s.…
The symmetric simple exclusion process (SEP) is a paradigmatic model of diffusion in a single-file geometry, in which the particles cannot cross. In this model, the study of currents have attracted a lot of attention. In particular, the…
We consider optimal approximation with respect to the mean square error of It\^o integrals and Skorohod integrals given an equidistant discretization of the Brownian motion. We obtain for suitable integrands optimal rates smaller than the…
We prove a strong duality result for a linear programming problem which has the interpretation of being a discretised optimal Skorokhod embedding problem, and we recover this continuous time problem as a limit of the discrete problems. With…
Given a family $(\mu_\lambda,\lambda\geq0)$ of integrable mean-zero probability measures such that, for every $\lambda\geq0$, $\mu_\lambda$ is the image of $\mu_1$ under the homothety $y\longmapsto\sqrt{\lambda}y$, we provide a necessary…
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
The CEV model is given by the stochastic differential equation $X_t=X_0+\int_0^t\mu X_sds+\int_0^t\sigma (X^+_s)^pdW_s$, $\frac{1}{2}\le p<1$. It features a non-Lipschitz diffusion coefficient and gets absorbed at zero with a positive…
We investigate the optimal stopping problems involving the supremum of a diffusion. The starting point is the link between works of Peskir and Meilijson, which we describe in a unified manner. The description developped follows mainly the…
In a recent work by Gross, it was proved that, given a distribution $\mu$ with zero mean and finite second moment, we can find a simply connected domain $\Omega$ such that if $Z_{t}$ is a standard planar BM, then…
We discuss restrictions on the existence of the diffusion pole in the translationally invariant diagrammatic treatment of disordered electron systems. We use the Bethe-Salpeter equations for the two-particle vertex in the electron-hole and…
Unlike $\mathbb{R}^{3}$, the homogeneous spaces $\mathbb{E}(-1,\tau)$ have a great variety of entire vertical minimal graphs. In this paper we explore conditions which guarantees that a minimal surface in $\mathbb{E}(-1,\tau)$ is such a…
We consider one-dimensional diffusions, with polynomial drift and diffusion coefficients, so that in particular the motion can be space-inhomogeneous, interacting via one-sided reflections. The prototypical example is the well-known model…
The paper is focused on the numerical solution of stochastic reaction-diffusion problems. A special attention is addressed to the conservation of mean-square dissipativity in the time integration of the spatially discretized problem,…
In this work, a complete error analysis is presented for fully discrete solutions of the subdiffusion equation with a time-dependent diffusion coefficient, obtained by the Galerkin finite element method with conforming piecewise linear…
The aim of this paper is to propose a methodology for testing general hypothesis in a Markovian setting with random sampling. A discrete Markov chain X is observed at random time intervals $\tau$ k, assumed to be iid with unknown…
Switching identities have a long history in potential theory and stochastic analysis. In recent work of Cox and Wang, a switching identity was used to connect an optimal stopping problem and the Skorokhod embedding problem (SEP). Typically…
The study of intermittency for the parabolic Anderson problem usually focuses on the moments of the solution which can describe the high peaks in the probability space. In this paper we set up the equation on a finite spatial interval, and…
We consider the time-harmonic elastic wave scattering from a general (possibly anisotropic) inhomogeneous medium with an embedded impenetrable obstacle. We show that the impenetrable obstacle can be effectively approximated by an isotropic…
The 1D Ising model is the simplest Hamiltonian-based model in statistical mechanics. The sim- plest interacting particle process is the Symmetric Exclusion Process (SEP), a 1D lattice gas of particles that hop symmetrically and cannot…
A one-dimensional, continuous, regular, and strong Markov process $X$ with state space $E$ hits any point $z \in E$ fast with positive probability. To wit, if $\tau_z = \inf \{t \geq 0:X_{t} = z\}$, then $P_\xi({ \tau}_z<\varepsilon)>0$ for…