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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.
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...
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...
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...
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...
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.
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 ...
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...
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...
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...
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...
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...
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.

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