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Let $S$ be a countable set provided with a partial order and a minimal element. Consider a Markov chain on $Scup{0}$ absorbed at $0$ with a quasi-stationary distribution. We use Holley inequality to obtain sufficient conditions under which the following hold. The trajectory of the chain starting from the minimal state is stochastically dominated by the trajectory of the chain starting from any probability on $S$, when both are conditioned to nonabsorption until a certain time. Moreover, the Yaglom limit corresponding to this deterministic initial condition is the unique minimal quasi-stationary distribution in the sense of stochastic order. As an application, we provide new proofs to classical results in the field.
We consider one-dimensional branching Brownian motion in which particles are absorbed at the origin. We assume that when a particle branches, the offspring distribution is supercritical, but the particles are given a critical drift towards the origin
Let ${u(t,,x)}_{tge 0, xin mathbb{R}^d}$ denote the solution of a $d$-dimensional nonlinear stochastic heat equation that is driven by a Gaussian noise, white in time with a homogeneous spatial covariance that is a finite Borel measure $f$ and satisf
Consider a parabolic stochastic PDE of the form $partial_t u=frac{1}{2}Delta u + sigma(u)eta$, where $u=u(t,,x)$ for $tge0$ and $xinmathbb{R}^d$, $sigma:mathbb{R}tomathbb{R}$ is Lipschitz continuous and non random, and $eta$ is a centered Gaussian no
As proved by Regnier and Rosler, the number of key comparisons required by the randomized sorting algorithm QuickSort to sort a list of $n$ distinct items (keys) satisfies a global distributional limit theorem. Fill and Janson proved results about th
We prove that all finite joint distributions of creation and annihilation operators in Monotone and anti-Monotone Fock spaces can be realized as Quantum Central Limit of certain operators on a $C^*$-algebra, at least when the test functions are Riema