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

  • Blackwell, David. A renewal theorem. Duke Math. J. 15, (1948). 145--150. MR0024093
  • Blackwell, David. Extension of a renewal theorem. Pacific J. Math. 3, (1953). 315--320. MR0054880
  • Bolthausen, Erwin. A central limit theorem for two-dimensional random walks in random sceneries. Ann. Probab. 17 (1989), no. 1, 108--115. MR0972774
  • Borodin, A. N. A limit theorem for sums of independent random variables defined on a recurrent random walk. (Russian) Dokl. Akad. Nauk SSSR 246 (1979), no. 4, 786--787. MR0543530
  • 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
  • Castell, Fabienne; Guillotin-Plantard, Nadine; Pène, Françoise; Schapira, Bruno. A local limit theorem for random walks in random scenery and on randomly oriented lattices. Ann. Probab. 39 (2011), no. 6, 2079--2118. MR2932665
  • Castell, F.; Guillotin-Plantard, N. and Pène, F.: Limit theorems for one and two-dimensional random walks in random scenery. phTo appear in Ann. Inst. H. Poincaré Probab. Statist., (2012).ARXIV1103.4453
  • Deligiannidis, G.; Utev, S. A. Computation of the asymptotics of the variance of the number of self-intersections of stable random walks using the Wiener-Darboux theory. (Russian) Sibirsk. Mat. Zh. 52 (2011), no. 4, 809--822; translation in Sib. Math. J. 52 (2011), no. 4, 639--650 MR2883216
  • den Hollander, Frank; Steif, Jeffrey E. Random walk in random scenery: a survey of some recent results. Dynamics & stochastics, 53--65, IMS Lecture Notes Monogr. Ser., 48, Inst. Math. Statist., Beachwood, OH, 2006. MR2306188
  • Erdös, P.; Feller, W.; Pollard, H. A property of power series with positive coefficients. Bull. Amer. Math. Soc. 55, (1949). 201--204. MR0027867
  • 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
  • Guibourg, D.: Théorèmes de renouvellement pour des fonctionnelles additives associées à des cha^ines de Markov fortement ergodiques. phPhd Thesis, Rennes University (2011). rlhttp://tel.archives-ouvertes.fr/tel-00583175
  • 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
  • Le Doussal, Pierre. Diffusion in layered random flows, polymers, electrons in random potentials, and spin depolarization in random fields. J. Statist. Phys. 69 (1992), no. 5-6, 917--954. MR1192029
  • Le Gall, Jean-François; Rosen, Jay. The range of stable random walks. Ann. Probab. 19 (1991), no. 2, 650--705. MR1106281
  • Matheron, G. and de Marsily G.: Is transport in porous media always diffusive? A counterxample. phWater Resources Res. 16, (1980), 901--907.
  • Schmidt, Klaus. On recurrence. Z. Wahrsch. Verw. Gebiete 68 (1984), no. 1, 75--95. MR0767446
  • Spitzer, Frank. Principles of random walk. The University Series in Higher Mathematics D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London 1964 xi+406 pp. MR0171290


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