The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. Billingsley, Patrick. Convergence of probability measures. John Wiley & Sons, Inc., New York-London-Sydney 1968 xii+253 pp. MR0233396 (38 #1718)

  2. Bolthausen, Erwin. A central limit theorem for two-dimensional random walks in random sceneries. Ann. Probab. 17 (1989), no. 1, 108--115. MR0972774 (90h:60020)

  3. Borodin, A. N. Limit theorems for sums of independent random variables defined on a transient random walk. (Russian) Investigations in the theory of probability distributions, IV. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 85 (1979), 17--29, 237, 244. MR0535455 (80j:60029)

  4. Borodin, A. N. Limit theorems for sums of independent random variables defined on a recurrent random walk. (Russian) Teor. Veroyatnost. i Primenen. 28 (1983), no. 1, 98--114. MR0691470 (84g:60033)

  5. Cadre, B. Etude de convergence en loi de fonctionnelles de processus: Formes quadratiques ou multilinéaires aléatoires, Temps locaux d'intersection de marches aléatoires, Théorème central limite presque sûr. (1995) PHD Thesis, Université Rennes 1.

  6. Chen, X. ; Khoshnevisan, D. From charged polymers to random walk in random scenery. (2009) To appear in Proceedings of the Third Erich L. Lehmann Symposium.

  7. Chen, Xia; Li, Wenbo V. Large and moderate deviations for intersection local times. Probab. Theory Related Fields 128 (2004), no. 2, 213--254. MR2031226 (2005m:60175)

  8. Cohen, S.; Dombry, C. Convergence of dependent walks in a random scenery to fBm-local time fractional stable motions. (2009) To appear in Journal of Mathematics of Kyoto University.

  9. Cohen, Serge; Samorodnitsky, Gennady. Random rewards, fractional Brownian local times and stable self-similar processes. Ann. Appl. Probab. 16 (2006), no. 3, 1432--1461. MR2260069 (2008b:60080)

  10. Dobrushin, R. L.; Major, P. Non-central limit theorems for nonlinear functionals of Gaussian fields. Z. Wahrsch. Verw. Gebiete 50 (1979), no. 1, 27--52. MR0550122 (81i:60019)

  11. Dombry,C. Convergence to stable noise and applications. (2009) Preprint.

  12. Dombry, C.; Guillotin-Plantard, N. Discrete approximation of a stable self-similar stationary increments process. (2009) Bernoulli, Vol. 15, No 1, 195--222.

  13. Guillotin-Plantard, N.; Le Ny, A. Transient random walks on 2d-oriented lattices. (2007) Theory of Probability and Its Applications (TVP), Vol. 52, No 4, 815—826.

  14. Guillotin-Plantard, Nadine; Le Ny, Arnaud. A functional limit theorem for a 2D-random walk with dependent marginals. Electron. Commun. Probab. 13 (2008), 337--351. MR2415142 (2009e:60079)

  15. Guillotin-Plantard, N.; Prieur, C. Central limit theorem for sampled sums of dependent random variables. (2009) To appear in ESAIM P\&S.

  16. Guillotin-Plantard, N.; Prieur, C. Limit theorem for random walk in weakly dependent random scenery. (2009) Preprint.

  17. Kesten, H.; Spitzer, F. A limit theorem related to a new class of self-similar processes. Z. Wahrsch. Verw. Gebiete 50 (1979), no. 1, 5--25. MR0550121 (82a:60149)

  18. Lang, Reinhard; Nguyen, Xuan-Xanh. Strongly correlated random fields as observed by a random walker. Z. Wahrsch. Verw. Gebiete 64 (1983), no. 3, 327--340. MR0716490 (86a:60046)

  19. Le Borgne, Stéphane. Exemples de systèmes dynamiques quasi-hyperboliques à décorrélations lentes. (French) [Examples of quasi-hyperbolic dynamical systems with slow decay of correlations] C. R. Math. Acad. Sci. Paris 343 (2006), no. 2, 125--128. MR2243306 (2007f:37041)

  20. Ledoux, Michel; Talagrand, Michel. Probability in Banach spaces. Isoperimetry and processes. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 23. Springer-Verlag, Berlin, 1991. xii+480 pp. ISBN: 3-540-52013-9 MR1102015 (93c:60001)

  21. Maejima, Makoto. Limit theorems related to a class of operator-self-similar processes. Nagoya Math. J. 142 (1996), 161--181. MR1399472 (97g:60033)

  22. Nualart, David. Stochastic integration with respect to fractional Brownian motion and applications. Stochastic models (Mexico City, 2002), 3--39, Contemp. Math., 336, Amer. Math. Soc., Providence, RI, 2003. MR2037156 (2004m:60119)

  23. Nualart, David. The Malliavin calculus and related topics. Second edition. Probability and its Applications (New York). Springer-Verlag, Berlin, 2006. xiv+382 pp. ISBN: 978-3-540-28328-7; 3-540-28328-5 MR2200233 (2006j:60004) 

  24. Pène, F. Transient random walk in $Z^2$ with stationary orientations. (2007) To appear in ESAIM P&S.

  25. Pipiras, Vladas; Taqqu, Murad S. Integration questions related to fractional Brownian motion. Probab. Theory Related Fields 118 (2000), no. 2, 251--291. MR1790083 (2002c:60091)

  26. Wang, Wensheng. Weak convergence to fractional Brownian motion in Brownian scenery. Probab. Theory Related Fields 126 (2003), no. 2, 203--220. MR1990054 (2004d:60265)

Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.