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Journal of Theoretical Probability

, Volume 32, Issue 1, pp 330–352 | Cite as

Limit Theorems for Local and Occupation Times of Random Walks and Brownian Motion on a Spider

  • Endre CsákiEmail author
  • Miklós Csörgő
  • Antónia Földes
  • Pál Révész
Article
  • 58 Downloads

Abstract

A simple random walk and a Brownian motion are considered on a spider that is a collection of half lines (we call them legs) joined at the origin. We give a strong approximation of these two objects and their local times. For fixed number of legs, we establish limit theorems for n-step local and occupation times.

Keywords

Spider Random walk Local time Occupation time Brownian motion 

Mathematics Subject Classification (2010)

Primary 60F05 60F15 60G50 Secondary 60J65 60J10 

Notes

Acknowledgements

We sincerely wish to thank the referee of our submission for careful reading our manuscript, and for making a number of insightful comments and suggestions that helped and prompted us to improve the presentation and proofs of our results when revising this paper for publication.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Alfréd Rényi Institute of MathematicsHungarian Academy of SciencesBudapestHungary
  2. 2.School of Mathematics and StatisticsCarleton UniversityOttawaCanada
  3. 3.Department of Mathematics, College of Staten IslandCUNYStaten IslandUSA
  4. 4.Institut für Statistik und WahrscheinlichkeitstheorieTechnische Universität WienViennaAustria

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