Generating discrete-time constrained random walks and Lévy flights

We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly ac...

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Bibliographic Details
Published in:Physical review. E 2021-08, Vol.104 (2), p.024117-024117, Article 024117
Main Authors: De Bruyne, Benjamin, Majumdar, Satya N., Schehr, Grégory
Format: Article
Language:English
Subjects:
Physics
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Summary:We introduce a method to exactly generate bridge trajectories for discrete-time random walks, with arbitrary jump distributions, that are constrained to initially start at the origin and return to the origin after a fixed time. The method is based on an effective jump distribution that implicitly accounts for the bridge constraint. It is illustrated on various jump distributions and is shown to be very efficient in practice. In addition, we show how to generalize the method to other types of constrained random walks such as generalized bridges, excursions, and meanders.
ISSN:2470-0045
2470-0053
DOI:10.1103/PhysRevE.104.024117