相关论文: Some Estimates for Planar Random Walk and Brownian…

We consider the approximation of the performance of random walks in the quarter-plane. The approximation is in terms of a random walk with a product-form stationary distribution, which is obtained by perturbing the transition probabilities…

We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by the generating functions of the values taken by the harmonic…

We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting…

This paper addresses the problem of estimating drift parameter of the Ornstein - Uhlenbeck type process, driven by the sum of independent standard and fractional Brownian motions. The maximum likelihood estimator is shown to be consistent…

We study random walks on sub-Riemannian manifolds using the framework of retractions, i.e., approximations of normal geodesics. We show that such walks converge to the correct horizontal Brownian motion if normal geodesics are approximated…

These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. After discussion of some classical methods, such as reflection…

A random walk problem with particles on discrete double infinite linear grids is discussed. The model is based on the work of Montroll and others. A probability connected with the problem is given in the form of integrals containing…

This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…

The problem of detecting a few anomalous processes among a large number of data streams is considered. At each time, aggregated observations can be taken from a chosen subset of the processes, where the chosen subset conforms to a given…

We measured the overall motion of Brownian particles suspended in water by a self-mixing thin-slice solid-state laser with extreme optical sensitivity. From the demodulated signal of laser intensity fluctuations through self-mixing…

The trace of a Markov process is the time changed process of the original process on the support of the Revuz measure used in the time change. In this paper, we will concentrate on the reflecting Brownian motions on certain closed strips.…

The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…

We give a series of combinatorial results that can be obtained from any two collections (both indexed by $\Z\times \N$) of left and right pointing arrows that satisfy some natural relationship. When applied to certain self-interacting…

We study the asymptotic behaviour of partial sums of long range dependent random variables and that of their counting process, together with an appropriately normalized integral process of the sum of these two processes, the so-called…

We investigate random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramer's condition. We prove moderate deviation principles in dimensions two and larger, covering…

Random walk in random environment (RWRE) is a fundamental model of statistical mechanics, describing the movement of a particle in a highly disordered and inhomogeneous medium as a random walk with random jump probabilities. It has been…

In a recent paper of Eichelsbacher and Koenig (2008) the model of ordered random walks has been considered. There it has been shown that, under certain moment conditions, one can construct a k-dimensional random walk conditioned to stay in…

A Brownian loop is a random walk circuit of infinitely many, suitably infinitesimal, steps. In a plane such a loop may or may not enclose a marked point, the origin, say. If it does so it may wind arbitrarily many times, positive or…

This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching…

This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…