Local probabilities for random walks conditioned to stay positive

Probability Theory and Related Fields

Volumn 143, Issue 1-2, 2009, Pages 177-217

  Vatutin, Vladimir A ^a   Wachtel, Vitali ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

Limit theorems; Random walks; Stable laws

Indexed keywords

EID: 54349104679     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-007-0124-8     Document Type: Article

References (24)

1. L. Alili L. Chaumont 2001 A new fluctuation identity for Levy processes and some applications Bernoulli 7 557 569
2. L. Alili R.A. Doney 1999 Wiener-Hopf factorization revisited and some applications Stoc. Stoc. Rep. 66 87 102
3. A.A. Borovkov 2004 On the asymptotics of distributions of first-passage times, II Math. Notes 75 322 330
4. Bingham N.H., Goldie C.M. and Teugels J.L. (1987). Regular Variation. Cambridge University Press, Cambridge, 494
5. A. Bryn-Jones R.A. Doney 2006 A functional limit theorem for random walk conditioned to stay non-negative J. Lond. Math. Soc. (2) 74 244 258
6. F. Caravenna 2005 A local limit theorem for random walks conditioned to stay positive Probab. Theory Relat. Fields 133 508 530
7. Caravenna, F., Chaumont, L.: Invariance principles for raandom walk conditioned to stay positive. Ann. Inst. Henri Poincare Probab. Statist. (2007, to appear)
8. Y.S. Chow 1986 On moments of ladder height variables Adv. Appl. Math. 7 46 54
9. R.A. Doney 1982 On the exact asymptotic behavior of the distribution of ladder epochs Stoch. Proc. Appl. 12 203 214
10. R.A. Doney 1982 On the existence of the mean ladder height for random walk Probab. Theory Relat. Fields 59 373 382
11. R.A. Doney 1985 Conditional limit theorems for asymptotically stable random walks Probab. Theory Relat. Fields 70 351 360
12. R.A. Doney 1995 Spitzer's condition and the ladder variables in random walks Probab. Theory Relat. Fields 101 577 580
13. R. Durrett 1978 Conditioned limit theorems for some null recurrent markov processes Ann. Probab. 6 798 827
14. M.S. Eppel 1979 A local limit theorem for the first overshoot Siberian Math. J. 20 130 138
15. Feller W. (1971). An Introduction to Probability Theory and its Applications, vol. 2. Willey, New York
16. P. Greenwood E. Omey J.L. Teugels 1982 Harmonic renewal measures and bivariate domains of attraction in fluctuation theorey Z. Wahrscheinlichkeitstheorie verw. Gebiete 61 527 539
17. A.A. Mogulskii B.A. Rogozin 2005 Local theorem for the first hitting time of a fixed level by a random walk Siberian Adv. Math. 15 3 1 27
18. D. Monrad M.L. Silverstein 1979 Stable processes: sample function growth at a local minimum Z. Wahrscheinlichkeitstheorie verw. Gebiete 49 177 210
19. Petrov V.V. (1975). Sums of Independent Random Variables. Springer, Berlin
20. B.A. Rogozin 1971 On the distrbution of the first ladder moment and height and fluctustions of a random walk Theory Probab. Appl. 16 575 595
21. Seneta, E.: Regularly varying functions. Lecture Notes in Mathematics, vol. 508. Springer, Berlin (1976)
22. Spitzer F. (1964). Principles of Random Walk. Van Nostrand, Princeton
23. Vatutin, V.A., Wachtel, V.: Local Limit Theorem for Ladder Epochs. WIAS Preprint 1200, (2007)
24. V.M. Zolotarev 1957 Mellin-Stiltjes transform in probability theory Theory Probab. Appl. 2 433 460