Two-boundary problems for a random walk with negative geometric jumps

T. V. Kadankova
2004 Theory of Probability and Mathematical Statistics  
Two-boundary problems for a random walk with negative geometric jumps are considered, and the corresponding results for a usual semicontinuous random walk are generalized for them. The following results are obtained: the probability distribution of ruin is found and expressed in terms of the lower and upper boundaries; formulas are given for the joint distribution of the infimum, supremum, and the walk itself at an arbitrary time instance; the transient probabilities and ergodic distribution
more » ... dic distribution are evaluated for the process describing the evolution of the random walk with two boundaries.
doi:10.1090/s0094-9000-04-00604-0 fatcat:dpvi6nyxtnachf5hhfzgpufacq