COMPLETE CORRECTED DIFFUSION APPROXIMATIONS FOR THE MAXIMUM OF A RANDOM WALK By

@inproceedings{Blanchet2006COMPLETECD,
  title={COMPLETE CORRECTED DIFFUSION APPROXIMATIONS FOR THE MAXIMUM OF A RANDOM WALK By},
  author={Jose Blanchet and Peter Glynn},
  year={2006}
}
Consider a random walk (Sn : n ≥ 0) with drift −µ and S0 = 0. Assuming that the increments have exponential moments, negative mean, and are strongly nonlattice, we provide a complete asymptotic expansion (in powers of µ > 0) that corrects the diffusion approximation of the all time maximum M = max n≥0 Sn. Our results extend both the first-order correction of Siegmund [Adv. We also show that the Cramér–Lundberg constant (as a function of µ) admits an analytic extension throughout a neighborhood… CONTINUE READING

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