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

  • Aurzada, Frank. A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights. Statist. Probab. Lett. 78 (2008), no. 15, 2300--2307. MR2462665
  • Aurzada, Frank; Lifshits, Mikhail. On the small deviation problem for some iterated processes. Electron. J. Probab. 14 (2009), no. 68, 1992--2010. MR2550290
  • Bingham, N. H.; Goldie, C. M.; Teugels, J. L. Regular variation. Encyclopedia of Mathematics and its Applications, 27. Cambridge University Press, Cambridge, 1987. xx+491 pp. ISBN: 0-521-30787-2 MR0898871
  • Bogachev, Vladimir I. Gaussian measures. Mathematical Surveys and Monographs, 62. American Mathematical Society, Providence, RI, 1998. xii+433 pp. ISBN: 0-8218-1054-5 MR1642391
  • Borell, Christer. Tail probabilities in Gauss space. Vector space measures and applications (Proc. Conf., Univ. Dublin, Dublin, 1977), I, pp. 73--82, Lecture Notes in Math., 644, Springer, Berlin-New York, 1978. MR0502400
  • C. Borell. On the Taylor series of a Wiener polynomial. Seminar notes on multiple stochastic integration, polynomial chaos and their integration. Case Western Reserve University, Cleveland, 1984.
  • Borovkov, A. A.; Ruzankin, P. S. On small deviations of series of weighted random variables. J. Theoret. Probab. 21 (2008), no. 3, 628--649. MR2425361
  • Chen, Xia; Kuelbs, James; Li, Wenbo. A functional LIL for symmetric stable processes. Ann. Probab. 28 (2000), no. 1, 258--276. MR1756005
  • Chung, Kai Lai. On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. 64, (1948). 205--233. MR0026274
  • Driver, Bruce K.; Gordina, Maria. Heat kernel analysis on infinite-dimensional Heisenberg groups. J. Funct. Anal. 255 (2008), no. 9, 2395--2461. MR2473262
  • Ikeda, Nobuyuki; Watanabe, Shinzo. Stochastic differential equations and diffusion processes. Second edition. North-Holland Mathematical Library, 24. North-Holland Publishing Co., Amsterdam; Kodansha, Ltd., Tokyo, 1989. xvi+555 pp. ISBN: 0-444-87378-3 MR1011252
  • Kuelbs, J.; Li, W. V. A functional LIL and some weighted occupation measure results for fractional Brownian motion. J. Theoret. Probab. 15 (2002), no. 4, 1007--1030. MR1937783
  • Kuelbs, James; Li, Wenbo. A functional LIL for stochastic integrals and the Lévy area process. J. Theoret. Probab. 18 (2005), no. 2, 261--290. MR2137043
  • Ledoux, Michel. Isoperimetry and Gaussian analysis. Lectures on probability theory and statistics (Saint-Flour, 1994), 165--294, Lecture Notes in Math., 1648, Springer, Berlin, 1996. MR1600888
  • Li, Wenbo V. Small ball probabilities for Gaussian Markov processes under the $L_ p$-norm. Stochastic Process. Appl. 92 (2001), no. 1, 87--102. MR1815180
  • Li, W. V.; Shao, Q.-M. Gaussian processes: inequalities, small ball probabilities and applications. Stochastic processes: theory and methods, 533--597, Handbook of Statist., 19, North-Holland, Amsterdam, 2001. MR1861734
  • Lifshits, M. A. On the lower tail probabilities of some random series. Ann. Probab. 25 (1997), no. 1, 424--442. MR1428515
  • M. A. Lifshits. Asymptotic behavior of small ball probabilities. In Theory of Probability and Mathematical Statistics. Proceedings of VII International Vilnius Conference, pages 453--468, 1999.
  • Lifshits, Mikhail A.; Linde, Werner. Small deviations of weighted fractional processes and average non-linear approximation. Trans. Amer. Math. Soc. 357 (2005), no. 5, 2059--2079 (electronic). MR2115091
  • Mayer-Wolf, Eddy; Zeitouni, Ofer. The probability of small Gaussian ellipsoids and associated conditional moments. Ann. Probab. 21 (1993), no. 1, 14--24. MR1207213
  • Nelson, Edward. The free Markoff field. J. Functional Analysis 12 (1973), 211--227. MR0343816
  • Nelson, Edward. Quantum fields and Markoff fields. Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971), pp. 413--420. Amer. Math. Soc., Providence, R.I., 1973. MR0337206
  • Rémillard, Bruno. On Chung's law of the iterated logarithm for some stochastic integrals. Ann. Probab. 22 (1994), no. 4, 1794--1802. MR1331204
  • Rozovskiĭ, L. V. On small deviation probabilities for sums of independent positive random variables. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 341 (2007), Veroyatn. i Stat. 11, 151--167, 232; translation in J. Math. Sci. (N. Y.) 147 (2007), no. 4, 6935--6945 MR2363592
  • Rozovskiĭ, L. V. On small deviations of sums of weighted positive random variables. (Russian) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 384 (2010), Veroyatnost i Statistika. 16, 212--224, 313; translation in J. Math. Sci. (N. Y.) 176 (2011), no. 2, 224--231 MR2749362
  • Shi, Z. Liminf behaviours of the windings and Lévy's stochastic areas of planar Brownian motion. Séminaire de Probabilités, XXVIII, 122--137, Lecture Notes in Math., 1583, Springer, Berlin, 1994. MR1329108
  • Zhang, Rongmao; Lin, Zhengyan. A functional LIL for $m$-fold integrated Brownian motion. Chinese Ann. Math. Ser. B 27 (2006), no. 4, 459--472. MR2250870
  • Zhang, Rong Mao; Lin, Zheng Yan. A functional LIL for integrated $\alpha$ stable process. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 2, 393--404. MR2591601


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