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References

  1. Alsmeyer, Gerold. Some relations between harmonic renewal measures and certain first passage times. Statist. Probab. Lett. 12 (1991), no. 1, 19--27. MR1116754 (92g:60117)
  2. Beljaev, Ju. K.; Maksimov, V. M. Analytical properties of a generating function for the number of renewals. (Russian) Teor. Verojatnost. i Primenen. 8 1963 108--112. MR0162298 (28 #5497)
  3. Borovkov, A. A. New limit theorems in boundary-value problems for sums of independent terms. (Russian) Sibirsk. Mat. Ž. 3 1962 645--694. MR0145568 (26 #3099)
  4. Chow, Yuan Shih; Teicher, Henry. Probability theory. Independence, interchangeability, martingales. Second edition. Springer Texts in Statistics. Springer-Verlag, New York, 1988. xviii+467 pp. ISBN: 0-387-96695-1 MR0953964 (89e:60001)
  5. Doney, R. A. Moments of ladder heights in random walks. J. Appl. Probab. 17 (1980), no. 1, 248--252. MR0557453 (80m:60074)
  6. Doney, R. A. On the asymptotic behaviour of first passage times for transient random walk. Probab. Theory Related Fields 81 (1989), no. 2, 239--246. MR0982656 (89m:60157)
  7. Doney, R. A. Last exit times for random walks. Stochastic Process. Appl. 31 (1989), no. 2, 321--331. MR0998121 (90g:60064)
  8. Feller, William. An introduction to probability theory and its applications. Vol. I. Third edition John Wiley & Sons, Inc., New York-London-Sydney 1968 xviii+509 pp. MR0228020 (37 #3604)
  9. Feller, William. An introduction to probability theory and its applications. Vol. II. Second edition John Wiley & Sons, Inc., New York-London-Sydney 1971 xxiv+669 pp. MR0270403 (42 #5292)
  10. Gut, Allan. Stopped random walks. Limit theorems and applications. Second edition. Springer Series in Operations Research and Financial Engineering. Springer, New York, 2009. xiv+263 pp. ISBN: 978-0-387-87834-8 MR2489436 (2010f:60131)
  11. Heyde, C. C. Two probability theorems and their application to some first passage problems. J. Austral. Math. Soc. 4 1964 214--222. MR0183004 (32 #486)
  12. Iksanov, A. and Meiners, M. Exponential rate of almost sure convergence of intrinsic martingales in supercritical branching random walks. J. Appl. Prob. 47 2010 513--525.
  13. Kesten, Harry; Maller, R. A. Two renewal theorems for general random walks tending to infinity. Probab. Theory Related Fields 106 (1996), no. 1, 1--38. MR1408415 (97i:60113)
  14. Pratt, John W. On interchanging limits and integrals. Ann. Math. Statist. 31 1960 74--77. MR0123673 (23 #A997)


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