Survival probability of a run-and-tumble particle in the presence of a drift

@article{DeBruyne2021SurvivalPO,
  title={Survival probability of a run-and-tumble particle in the presence of a drift},
  author={Benjamin De Bruyne and Satya N. Majumdar and Gr{\'e}gory Schehr},
  journal={Journal of Statistical Mechanics: Theory and Experiment},
  year={2021},
  volume={2021}
}
We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate γ, the (new) velocity of the particle is drawn randomly from a distribution W(v). We study the survival probability S(x, t) of a particle starting from x ⩾ 0 up to time t and obtain an explicit expression for its double Laplace transform (with respect to both x and t) for an arbitrary velocity… 

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