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Simulating the Maximum of a Random Walk
Random walk Single-server queue Simulation Stationary distribution
2015/7/8
In this paper, we show how to exactly sample from the distribution of the maximum of a random walk with negative drift. We also explore related variance reduction methods.
Diffusion Approximations for the Maximum of a Perturbed Random Walk
Perturbed random walk diffusion approximation light-tailed distributi
2015/7/6
Considera random walk S=(Sn:n≥O) that is "perturbed" by a stationary sequence (ξn:n≥O) to produce the process S=(Sn+ξn:n≥O). In this paper, we are concerned with developing limit theorems and approxim...
Tail Asymptotics for the Maximum of Perturbed Random Walk
Perturbed random walk Cramér–Lundberg approximation coupling heavy tails
2015/7/6
Consider a random walk S = (Sn:n≥0) that is “perturbed” by a stationary sequence (ξn:n≥0) to produce the process (Sn+ξn:n≥0). This paper is concerned with computing the distribution of the all-time ma...
Complete Corrected Diffusion Approximations for the Maximum of a Random Walk
Corrected diffusion approximations random walks ladder heights single-server queue
2015/7/6
Consider a random walk (Sn: n ≥ 0) with drift −μ and S0= 0. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic ex...
A random walk on image patches
image patches di usion maps Laplacian eigenmaps graph Laplacian
2011/7/19
In this paper we address the problem of understanding the success of algorithms that organize patches according to graph-based metrics. Algorithms that analyze patches extracted from images or time se...
A Random Walk with Drift: Interview with Peter J. Bickel
Random Walk Interview Peter J. Bickel
2011/7/5
I met Peter J. Bickel for the first time in 1981. He came to Jerusalem for a year; I had just started working on my Ph.D. studies.
A self-similar process arising from a random walk with random environment in random scenery
birth–death process random environment random scenery random walk self-similar process
2011/3/24
In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion ...
The ladder variables of a Markov random walk
Markov random walks ladder variables Harris recurrence regeneration epochs coupling
2009/9/22
Given a Harris chain (M,,)n40 on any state space
(9C,) with essentially unique stationary measure <, let (Xn)nZObe
a sequence of real-valued random variables which are conditionally
independent, gi...
The existence of a steady state for perturbed symmetric random walk on a random lattice
Random field passive tracer random walk in random environment Einstein relation
2009/9/21
In the present paper we consider a continuous time
random walk on an anisotropic random lattice. We show the existence
of a steady state 0, for the environment process (( (t)),ao corresponding
to t...
ON TWE RENlARRABLE DISTRIBUTIONS OF MAXIPMA OF SOME FRAGMENTS OF THE STANI)ARD REFLECTING RANDOM WALK AND BROWNIAN MOTION
Standard random walk standard Brownian motion excursion meander comeander infinite divisibility
2009/9/18
In this paper, we consider some distributions of maxima
of excursions and related variables for standard random walk and
Brownian motion. We discuss the infinite divisibility properties of
these di...
Random walk in deterministically changing environment
Random Walk Random environment Dynamical Systems CLT Transfer operator
2009/6/12
We consider a random walk with transition probabilities weakly dependent on an environment with a deterministic,but strongly chaotic,evolution.We prove that for almost all initial conditions of the en...
On the Speed of the One-dimensional Excited Random Walk in the Transient Regime
Excited Random Walk Pertubed Random Walk Law of Large Numbers
2009/6/12
We study a class of nearest-neighbor discrete time integer random walks introduced by Zerner (2005), the so called multi-excited random walks. The jump probabilities for such random walker have a drif...
On the scaling limit of simple random walk excursion measure in the plane
Brownian excursion measure Brownian motion simple random walk excursion measure excursion Poisson kernel strong approximation scaling limit
2009/6/12
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...
Random Walk in Dynamic Markovian Random Environment
Random Walk Markovian Random Environment
2009/6/12
Random Walk in Dynamic Markovian Random Environment.
Ballistic random walk in a random environment with a forbidden direction
ballistic random walk random environment forbidden direction
2009/6/12
Ballistic random walk in a random environment with a forbidden.