𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The length of an excursion above a linear boundary by a random walk

✍ Scribed by Travis Lee; Max Minzner; Evan Fisher

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
249 KB
Volume
34
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

We consider random walks with steps that are independent and identically distributed with finite mean. The distribution and expected value of the length of an excursion that begins with the first step is investigated.

πŸ“œ SIMILAR VOLUMES

On the fragmentation of a torus by rando
On the fragmentation of a torus by random walk
✍ Augusto Teixeira; David Windisch πŸ“‚ Article πŸ“… 2011 πŸ› John Wiley and Sons 🌐 English βš– 413 KB

## Abstract We consider a simple random walk on a discrete torus \input amssym $({\Bbb Z}/N{\Bbb Z})^d$ with dimension __d__ β‰₯ 3 and large side length __N__. For a fixed constant __u__ β‰₯ 0, we study the percolative properties of the vacant set, consisting of the set of vertices not visited by the r

On the number of distinct sites visited
On the number of distinct sites visited by a random walk
✍ M. D. Donsker; S. R. S. Varadhan πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 727 KB

In the expression for a(?), M is a symmetric measure on the unit ball means that the support of M spans &. Let {rjl} be the n-step transition probabilities. It follows from hypotheses (i) and (ii) above that for any j e Z d there exists an no such that .rrYu>O. Moreover, from hypothesis (ii) it fol