Related papers: Discrete Hammersley's Lines with sources and sinks

We consider the simple exclusion process on Z x {0, 1}, that is, an ''horizontal ladder'' composed of 2 lanes, depending on 6 parameters. Particles can jump according to a lane-dependent translation-invariant nearest neighbour jump kernel,…

We obtain bounded for all $t$ solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on $(-L,L)$, with $L \rightarrow \infty$. We derive a priori estimates for the Dirichlet problems,…

We present a method of deriving linearizing transformations for a class of second order nonlinear ordinary differential equations. We construct a general form of a nonlinear ordinary differential equation that admits Bernoulli equation as…

We consider the discrete Hammersley-Aldous-Diaconis process (HAD) and the totally asymmetric simple exclusion process (TASEP) in Z. The basic coupling induces a multiclass process which is useful in discussing shock measures and other…

We consider a sequence of finite irreducible Markov chains with exponentially small transition rates: the transition graph is a fixed, finite, strongly connected directed graph; the transition rates decay exponentially on a paramenter N…

We consider invariant transports of stationary random measures on $\mathbb{R}^d$ and establish natural mixing criteria that guarantee persistence of asymptotic variances. To check our mixing assumptions, which are based on two-point Palm…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

In this work we introduce the discrete-space broken line process (with discrete and continues parameter values) and derive some of its properties. We explore polygonal Markov fields techniques developed by Arak-Surgailis. The discrete…

We derive the discrete version of the classical Helmholtz condition. Precisely, we state a theorem characterizing second order finite differences equations admitting a Lagrangian formulation. Moreover, in the affirmative case, we provide…

In this paper we consider a discrete-time dynamical system on the real line by random iteration of two functions. These functions are assumed to satisfy appropriate monotonicity conditions; optionally, a symmetry condition may be imposed.…

We develop a general framework for establishing non-uniqueness of stationary measures for stochastically forced dynamical systems possessing an almost surely invariant submanifold. Our main abstract result provides sufficient conditions for…

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…

We consider an Asymmetric Exclusion Process evolving on parallel mutually interacting lanes with neighbouring nearest hoppings of hardcore particles. Number of particles on each lane is conserved. We find a choice of the hopping rates, for…

We consider a locally uniformly strictly elliptic second order partial differential operator in $\mathbb{R}^d$, $d\ge 2$, with low regularity assumptions on its coefficients, as well as an associated Hunt process and semigroup. The Hunt…

We construct a stationary random tree, embedded in the upper half plane, with prescribed offspring distribution and whose vertices are the atoms of a unit Poisson point process. This process which we call Hammersley's tree process extends…

Here we develop a first order autoregressive model {Xn} that is marginally stationary where Xn is the sum/ extreme of k i.i.d observations. We prove that stationary solutions to these models are either semi-selfdecomposable/…

We provide a new result on the existence of extremal solutions for second-order Dirichlet problems with deviation argument. As a novelty in this work, the nonlinearity need not be continuous or monotone. In order to obtain this new result,…

This paper shows that a finite discrete convolution involving Stirling numbers of both kinds and harmonic numbers can be expressed in terms of the Bernoulli numbers. As applications of this expression, the linear recurrence relation for the…

It is shown by constructing Rohlins canonical measures that for a strictly stationary, d-dimensional vector-valued process X there exists another strictly stationary d-dimensional process U with uniform one-dimensional marginals and with…

We show that, for a stationary version of Hammersley's process, with Poisson ``sources'' on the positive x-axis, and Poisson ``sinks'' on the positive y-axis, an isolated second-class particle, located at the origin at time zero, moves…