Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 54, Issue 38, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/ac1d8e
Keywords
random walks; fluctuations; Brownian motion
Categories
Funding
- Luxembourg National Research Fund (FNR) [14548297]
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The proposed method generates bridge run-and-tumble trajectories with specified starting and ending conditions for different types of constrained particles, showing high efficiency in numerical implementation.
We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the concept of effective Langevin equations, valid for Markovian stochastic processes such as Brownian motion, to a non-Markovian stochastic process driven by a telegraphic noise, with exponentially decaying correlations. We obtain effective space-time dependent tumbling rates that implicitly accounts for the bridge constraint. We extend the method to other types of constrained run-and-tumble particles such as excursions and meanders. The method is implemented numerically and is shown to be very efficient.
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