Limit laws of transient excited random walks on integers

DOI10.1214/10-AIHP376zbMath1215.60057arXiv0908.4356MaRDI QIDQ537140

Elena Kosygina, Thomas S. Mountford

Publication date: 19 May 2011

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.4356

zbMATH Keywords

diffusion approximationbranching processlimit theoremstable lawexcited random walk

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Diffusion processes (60J60) Processes in random environments (60K37) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

Related Items (11)

Random walks with occasionally modified transition probabilities ⋮ Speed of excited random walks with long backward steps ⋮ Excited random walks with non-nearest neighbor steps ⋮ Convergence and nonconvergence of scaled self-interacting random walks to Brownian motion perturbed at extrema ⋮ Excited mob ⋮ Long range one-cookie random walk with positive speed ⋮ Excited random walk in a Markovian environment ⋮ On a general many-dimensional excited random walk ⋮ Extreme slowdowns for one-dimensional excited random walks ⋮ Random walks with local memory ⋮ Convergence of random walks with Markovian cookie stacks to Brownian motion perturbed at extrema

Cites Work

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• On the speed of a cookie random walk
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• Brownian motion and random walk perturbed at extrema
• Pathwise uniqueness for perturbed versions of Brownian motion and reflected Brownian motion
• Excited random walk
• Monotonicity for excited random walk in high dimensions
• Recurrence and transience of excited random walks on \(\mathbb Z^d\) and strips
• Central limit theorem for the excited random walk in dimension \(d\geq 2\)
• Multi-excited random walks on integers
• Random Walk in a One-Dimensional Random Medium
• Probability

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