Sergey G. Foss, Anatolii A. Puhalskii
Published 2007-12-17, updated 2012-08-17Version 3
We consider a random walk with a negative drift and with a jump distribution which under Cram\'er's change of measure belongs to the domain of attraction of a spectrally positive stable law. If conditioned to reach a high level and suitably scaled, this random walk converges in law to a nondecreasing Markov process which can be interpreted as a spectrally-positive L\'evy %-Khinchin process conditioned not to overshoot level one.
Journal: Stochastic Processes and Their Applications, 1221 (2011), 288-313
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