Directionally Reinforced Random Walks

@article{Mauldin1996DirectionallyRR,
  title={Directionally Reinforced Random Walks},
  author={R. Daniel Mauldin and Michael Monticino and Heinrich v. Weizs{\"a}cker},
  journal={Advances in Mathematics},
  year={1996},
  volume={117},
  pages={239-252}
}
Abstract This paper introduces and analyzes a class of directionally reinforced random walks. The work is motivated by an elementary model for time and space correlations in ocean surface wave fields. We develop some basic properties of these walks. For instance, we investigate recurrence properties and give conditions under which the limiting continuous versions of the walks are Gaussian diffusion processes. 

Limit Distributions of Directionally Reinforced Random Walks

Abstract As a mathematical model for time and space correlations in ocean surface wave fields, Mauldin, Monticino, and von Weizsacker (1996,Adv. in Math.117, 239–252), introduced directionally

On a directionally reinforced random walk

We consider a generalized version of a directionally reinforced random walk, which was originally introduced by Mauldin, Monticino, and von Weizsacker in [20]. Our main result is a stable limit

Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian

Persistent random walks

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study

Walks in rigid environments: symmetry and dynamics

— We study dynamical systems generated by a motion of a particle in an array of scatterers distributed in a lattice. Such deterministic cellular automata are called Lorentz-type lattice gases or

Senile reinforced random walks

THE SCALING LIMIT OF SENILE REINFORCED RANDOM WALK.

This paper proves that the scaling limit of nearest-neighbour senile reinforced random walk is Brownian Motion when the time T spent on the first edge has finite mean. We show that under suitable

A DIFFUSION LIMIT FOR GENERALIZED CORRELATED RANDOM WALKS

A generalized correlated random walk is a process of partial sums Xk = k P j=1 Y j such that (X;Y ) forms a Markov chain. For a sequence (X n ) of such processes where each Y n j takes only two

Variable Length Markov Chains, Persistent Random Walks: A Close Encounter

This is the story of the encounter between two worlds: the world of random walks and the world of Variable Length Markov Chains (VLMC). The meeting point turns around the semi-Markov property of

Optimal stopping rules for directionally reinforced processes

This paper analyzes optimal single and multiple stopping rules for a class of correlated random walks that provides an elementary model for processes exhibiting momentum or directional reinforcement

References

SHOWING 1-10 OF 11 REFERENCES

Principles Of Random Walk

This book is devoted exclusively to a very special class of random processes, namely to random walk on the lattice points of ordinary Euclidean space. The author considered this high degree of

Phase transition in reinforced random walk and RWRE on trees

On donne a une marche aleatoire sur un arbre infini une sorte particuliere de retroaction positive de telle sorte que les aretes deja traversees aient plus de chances d'etre traversees dans le futur.

On recurrence of a random walk in the plane

The purpose of this note is to establish a sufficient condition for recurrence of a random walk (Se) in R2. It follows from it that if SI/nn/2 is asymptotically normal then we have recurrence. Let

Convergence of Probability Measures

  • P. M. Lee
  • Mathematics
    The Mathematical Gazette
  • 1970
Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

An Introduction to Probability Theory and Its Applications

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to

A Course in Probability Theory

TLDR
This edition of A Course in Probability Theory includes an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.

Note on a class of one-dimensional reinforced r andom walks (preprint)

  • Note on a class of one-dimensional reinforced r andom walks (preprint)
  • 1991

On the statistical distribution of the heights of sea waves

  • Journal of Marine Research
  • 1952