相关论文: First passage process of a Markov additive process…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
Since diffusion processes arise in so many different fields, efficient tech-nics for the simulation of sample paths, like discretization schemes, represent crucial tools in applied probability. Such methods permit to obtain approximations…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
The property that a Jacobi matrix is reflectionless is usually characterized either in terms of Weyl m-functions or the vanishing of the real part of the boundary values of the diagonal matrix elements of the resolvent. We introduce a…
We consider two reflecting diffusion processes $(X_t)_{t \ge 0}$ with a moving reflection boundary given by a non-decreasing pure jump Markov process $(R_t)_{t \ge 0}$. Between the jumps of the reflection boundary the diffusion part behaves…
In any Markov chain with finite state space the distribution of transition records always belongs to the exponential family. This observation is used to prove a fluctuation theorem, and to show that the dynamical entropy of a stationary…
The asymmetric simple exclusion process (ASEP) is a model for translation in protein synthesis and traffic flow; it can be defined as a Markov chain describing particles hopping on a one-dimensional lattice. In this article I give an…
Multiple scattering of waves presents challenges for imaging complex media but offers potential for their characterization. Its onset is actually governed by the scattering mean free path $\ell_s$ that provides crucial information on the…
The goal of this paper is to identify exponential convergence rates and to find computable bounds for them for Markov processes representing unreliable Jackson networks. First we use the bounds of Lawler and Sokal in order to show that, for…
We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…
We develop a method for deriving thermodynamic bounds for first-passage problems of currents with two boundaries in Markov chains. Using this method, we derive a thermodynamic bound on the rate of dissipation in terms of the splitting…
The contribution from quantum vacuum fluctuations of a real massless scalar field to the motion of a test particle that interacts with the field in the presence of a perfectly reflecting flat boundary is here investigated. There is no…
The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional lattice of N sites. It is partially asymmetric…
A photon entering a scattering medium executes a three-dimensional random walk determined by the Henyey-Greenstein phase function. The photon either reaches the boundary for a first passage or is absorbed. Projecting the walk onto the axial…
We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing…
A survey of a variety of computational procedures for finding the mean first passage times in Markov chains is presented. The author recently developed a new accurate computational technique, an Extended GTH Procedure, Hunter (Special…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
A one - dimensional iterative map with two control parameters, i.e. the Kim - Kong map, is proposed. Our purpose is to investigate the characteristic properties of this map, and to discuss numerically the multifractal behavior of the…
For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…
For a stochastic process $(X_t)_{t\geq 0}$ we establish conditions under which the inverse first-passage time problem has a solution for any random variable $\xi >0$. For Markov processes we give additional conditions under which the…