Random walks reaching against all odds the other side of the quarter plane

@article{Leeuwaarden2013RandomWR,
  title={Random walks reaching against all odds the other side of the quarter plane},
  author={Johan van Leeuwaarden and Kilian Raschel},
  journal={Journal of Applied Probability},
  year={2013},
  volume={50},
  pages={85-102}
}
  • Johan van Leeuwaarden, Kilian Raschel
  • Published 2013
  • Mathematics
  • Journal of Applied Probability
  • For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact expression for the probability of this event, and derive an asymptotic expression for the case when $i_0$ becomes large, a situation in which the event becomes highly unlikely. The exact expression follows from the solution of a boundary value problem and is… CONTINUE READING

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