Publication Cover
Stochastics
An International Journal of Probability and Stochastic Processes
Volume 85, 2013 - Issue 6
91
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

On the number of empty boxes in the Bernoulli sieve I

Pages 946-959 | Received 13 Apr 2011, Accepted 24 Apr 2012, Published online: 21 Jun 2012

References

  • Anderson , K.K. and Athreya , K.B. 1987 . A renewal theorem in the infinite mean case . Ann. Probab. , 15 : 388 – 393 .
  • Bahadur , R.R. 1971 . Some Limit Theorems in Statistics. CBMS Regional Conference Series in Applied Mathematics , Vol. 4 , Philadelphia, PA : SIAM .
  • Bertoin , J. and Yor , M. 2005 . Exponential functionals of Lévy processes . Probab. Surveys , 2 : 191 – 212 .
  • Bingham , N.H. 1973 . Maxima of sums of random variables and suprema of stable processes . Z. Wahrsch. Verw. Gebiete. , 26 : 273 – 296 .
  • Bingham , N.H. , Goldie , C.M. and Teugels , J.L. 1989 . Regular Variation , Cambridge : Cambridge University Press .
  • Durrett , R. and Liggett , T.M. 1983 . Fixed points of the smoothing transformation . Z. Wahrsch. Verw. Gebiete. , 64 : 275 – 301 .
  • Feller , W. 1971 . An Introduction to Probability Theory and its Applications , 2nd ed. , Vol. 2 , New York : John Wiley & Sons .
  • Gnedin , A. , Iksanov , A. and Marynych , A. 2010 . Limit theorems for the number of occupied boxes in the Bernoulli sieve . Theory Stoch. Process. , 16 ( 32 ) : 44 – 57 .
  • Gnedin , A. , Iksanov , A. and Marynych , A. 2010 . The Bernoulli sieve: An overview . Discr. Math. Theoret. Comput. Sci. Proc. Ser. , AM : 329 – 342 .
  • Gnedin , A. , Iksanov , A. , Negadajlov , P. and Roesler , U. 2009 . The Bernoulli sieve revisited . Ann. Appl. Probab. , 19 : 1634 – 1655 .
  • Gradinaru , M. , Roynette , B. , Vallois , P. and Yor , M. 1999 . Abel transform and integrals of Bessel local times . Ann. Inst. Henri Poincaré , 35 : 531 – 572 .
  • Iksanov , A. 2012 . On the number of empty boxes in the Bernoulli sieve II . Stoch. Proc. Appl. , 122 : 2701 – 2729 .
  • Iksanov , A. and Möhle , M. 2008 . On the number of jumps of random walks with a barrier . Adv. Appl. Probab. , 40 : 206 – 228 .
  • Iksanov , A. and Negadajlov , P. 2008 . On the number of zero increments of random walks with a barrier . Discr. Math. Theoret. Comput. Sci. Proc. Ser. , AG : 247 – 254 .
  • Kaplan , N. 1975 . Limit theorems for a GI/G/∞ queue . Ann. Probab. , 3 : 780 – 789 .
  • Konstantopoulos , T. and Lin , S. 1998 . Macroscopic models for long-range dependent network traffic . Queueing Syst. , 28 : 215 – 243 .
  • Magdziarz , M. 2009 . Stochastic representation of subdiffusion processes with time-dependent drift . Stoch. Proc. Appl. , 119 : 3238 – 3252 .
  • Mikosch , T. and Resnick , S. 2006 . Activity rates with very heavy tails . Stoch. Proc. Appl. , 116 : 131 – 155 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.