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. Bass R. F., Chen. X and Rosen. J, Moderate deviations and laws of the iterated logarithm for the renormalized self-intersection local times of planar random walks. Electron. J. Probab., 11(2006), 993-1030. Math. Review 2007m:60064 MR2261059
  2. Bass, Richard F.; Chen, Xia; Rosen, Jay. Moderate deviations for the range of planar random walks. Mem. Amer. Math. Soc. 198 (2009), no. 929, viii+82 pp. ISBN: 978-0-8218-4287-4 MR2493313
  3. Bass, Richard F.; Kumagai, Takashi. Laws of the iterated logarithm for the range of random walks in two and three dimensions. Ann. Probab. 30 (2002), no. 3, 1369--1396. MR1920111 (2003d:60086)
  4. Bass, Richard F.; Rosen, Jay. An almost sure invariance principle for the range of planar random walks. Ann. Probab. 33 (2005), no. 5, 1856--1885. MR2165582 (2006h:60076)
  5. van den Berg, M. On the expected volume of intersection of independent Wiener sausages and the asymptotic behaviour of some related integrals. J. Funct. Anal. 222 (2005), no. 1, 114--128. MR2129767 (2006e:60117)
  6. van den Berg, Michiel; Bolthausen, Erwin. Asymptotics of the generating function for the volume of the Wiener sausage. Probab. Theory Related Fields 99 (1994), no. 3, 389--397. MR1283118 (95h:60121)
  7. van den Berg, M.; Bolthausen, E.; den Hollander, F. Moderate deviations for the volume of the Wiener sausage. Ann. of Math. (2) 153 (2001), no. 2, 355--406. MR1829754 (2002f:60041)
  8. van den Berg, M.; Bolthausen, E.; den Hollander, F. On the volume of the intersection of two Wiener sausages. Ann. of Math. (2) 159 (2004), no. 2, 741--782. MR2081439 (2005j:60050)
  9. van den Berg M. and Toth. B. Exponential estimates for the Wiener sausage. Probab. Theory Relat. Fields, 88 (1991), 249-259. Math. Review 92b:60075 MR1096482
  10. Bolthausen, E. On the volume of the Wiener sausage. Ann. Probab. 18 (1990), no. 4, 1576--1582. MR1071810 (92e:60151)
  11. Chen, Xia. Exponential asymptotics and law of the iterated logarithm for intersection local times of random walks. Ann. Probab. 32 (2004), no. 4, 3248--3300. MR2094445 (2005m:60174)
  12. Chen, Xia. Moderate deviations and law of the iterated logarithm for intersections of the ranges of random walks. Ann. Probab. 33 (2005), no. 3, 1014--1059. MR2135311 (2006d:60050)
  13. Chen. X, Random walk intersections: large deviations and some related topics. Preprint, 2008. Math. Review number not available.
  14. 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)
  15. Csáki, E.; Hu, Y. Strong approximations of three-dimensional Wiener sausages. Acta Math. Hungar. 114 (2007), no. 3, 205--226. MR2296543 (2007k:60085)
  16. Dembo, Amir; Zeitouni, Ofer. Large deviations techniques and applications.Second edition.Applications of Mathematics (New York), 38. Springer-Verlag, New York, 1998. xvi+396 pp. ISBN: 0-387-98406-2 MR1619036 (99d:60030)
  17. Donsker M. D. and S. R. S. Varadhan, Asymptotics for the Wiener sausage. Comm. Pure Appl. Math., 28 (1975), 525-565. Math. Review 53\#1757a MR0397901
  18. Le Gall, J.-F. Propriétés d'intersection des marches aléatoires. I. Convergence vers le temps local d'intersection.(French) [Intersection properties of random walks. I. Convergence to local time of intersection] Comm. Math. Phys. 104 (1986), no. 3, 471--507. MR0840748 (88d:60182)
  19. Le Gall, J.-F. Propriétés d'intersection des marches aléatoires. II. Étude des cas critiques.(French) [Intersection properties of random walks. II. Critical cases] Comm. Math. Phys. 104 (1986), no. 3, 509--528. MR0840749 (88d:60183)
  20. Le Gall, Jean-François. Sur la saucisse de Wiener et les points multiples du mouvement brownien.(French) [Wiener sausages and multiple points in Brownian motion] Ann. Probab. 14 (1986), no. 4, 1219--1244. MR0866344 (88e:60097)
  21. Le Gall, Jean-François. Fluctuation results for the Wiener sausage. Ann. Probab. 16 (1988), no. 3, 991--1018. MR0942751 (90a:60080)
  22. Le Gall, J.-F. Sur une conjecture de M. Kac.(French) [On a conjecture of M. Kac] Probab. Theory Related Fields 78 (1988), no. 3, 389--402. MR0949180 (89m:60195)
  23. Le Gall, Jean-François. Some properties of planar Brownian motion. École d'Été de Probabilités de Saint-Flour XX---1990, 111--235, Lecture Notes in Math., 1527, Springer, Berlin, 1992. MR1229519 (94g:60156)
  24. Le Gall, Jean-François; Rosen, Jay. The range of stable random walks. Ann. Probab. 19 (1991), no. 2, 650--705. MR1106281 (92j:60083)
  25. Hamana, Yuji; Kesten, Harry. A large-deviation result for the range of random walk and for the Wiener sausage. Probab. Theory Related Fields 120 (2001), no. 2, 183--208. MR1841327 (2002e:60161)
  26. König, Wolfgang; Mörters, Peter. Brownian intersection local times: upper tail asymptotics and thick points. Ann. Probab. 30 (2002), no. 4, 1605--1656. MR1944002 (2003m:60230)
  27. Spitzer, Frank. Electrostatic capacity, heat flow, and Brownian motion. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 3 1964 110--121. MR0172343 (30 #2562)
  28. Sznitman, Alain-Sol. Long time asymptotics for the shrinking Wiener sausage. Comm. Pure Appl. Math. 43 (1990), no. 6, 809--820. MR1059329 (92e:60152)
  29. Taylor, S. J. Multiple points for the sample paths of the symmetric stable process. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 5 1966 247--264. MR0202193 (34 #2066)


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