# 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} }

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

#### Citations

##### Publications citing this paper.

SHOWING 1-5 OF 5 CITATIONS

## Asymptotics for the Time of Ruin in the War of Attrition

VIEW 1 EXCERPT

CITES BACKGROUND

## A Correction Note for Price Dynamics in a Markovian Limit Order Market

VIEW 3 EXCERPTS

CITES BACKGROUND

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 20 REFERENCES

## Spontaneous symmetry breaking: exact results for a biased random walk model of an exclusion process

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## A mixture of the exclusion process and the voter model

VIEW 3 EXCERPTS

## Random Walks in the Quarter-Plane: Algebraic Methods, Boundary Value Problems and Applications

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL