Free Access
Volume 16, 2012
Page(s) 1 - 24
Published online 09 March 2012
  1. R.J. Adler, The Geometry of Random Fields. Wiley, New York (1981). [Google Scholar]
  2. H. Allouba and W. Zheng, Brownian-time processes : the pde connection and the half-derivative generator. Ann. Probab. 29 (2001) 1780–1795. [CrossRef] [Google Scholar]
  3. F. Aurzada and M. Lifshits, On the Small deviation problem for some iterated processes. Electron. J. Probab. 14 (2009) 1992–2010. [Google Scholar]
  4. B. Baeumer, M.M. Meerschaert and E. Nane, Brownian subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 361 (2009) 3915–3930. [CrossRef] [Google Scholar]
  5. B. Baeumer, M.M. Meerschaert and E. Nane, Space-time duality for fractional diffusion. J. Appl. Probab. 46 (2009) 1100–1115. [CrossRef] [Google Scholar]
  6. L. Beghin, L. Sakhno and E. Orsingher, Equations of Mathematical Physics and composition of Brownian and Cauchy processes. Stoch. Anal. Appl. 29 (2011) 551–569. [CrossRef] [Google Scholar]
  7. S.M. Berman, Local times and sample function properties of stationary Gaussian processes. Trans. Amer. Math. Soc. 137 (1969) 277–299. [CrossRef] [MathSciNet] [Google Scholar]
  8. S.M. Berman, Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J. 23 (1973) 69–94. [CrossRef] [Google Scholar]
  9. J. Bertoin, Lévy Processes. Cambridge University Press (1996). [Google Scholar]
  10. K. Burdzy, Some path properties of iterated Brownian motion, in Seminar on Stochastic Processes, edited by E.Çinlar, K.L. Chung and M.J. Sharpe. Birkhäuser, Boston (1993) 67–87. [Google Scholar]
  11. K. Burdzy and D. Khoshnevisan, The level set of iterated Brownian motion, Séminaire de Probabilités XXIX, edited by J. Azéma, M. Emery, P.-A. Meyer and M. Yor. Lect. Notes Math. 1613 (1995) 231–236. [Google Scholar]
  12. K. Burdzy and D. Khoshnevisan, Brownian motion in a Brownian crack. Ann. Appl. Probab. 8 (1998) 708–748. [CrossRef] [Google Scholar]
  13. E. Csáki, M. Csörgö, A. Földes and P. Révész, The local time of iterated Brownian motion. J. Theoret. Probab. 9 (1996) 717–743. [CrossRef] [MathSciNet] [Google Scholar]
  14. J. Cuzick and J. DuPreez, Joint continuity of Gaussian local times. Ann. Probab. 10 (1982) 810–817. [CrossRef] [Google Scholar]
  15. Y. Davydov, The invariance principle for stationary processes. Teor. Verojatnost. i Primenen. 15 (1970) 498–509. [Google Scholar]
  16. R.D. DeBlassie, Higher order PDE’s and symmetric stable processes. Probab. Theory Relat. Fields 129 (2004) 495–536. [Google Scholar]
  17. R.D. DeBlassie, Iterated Brownian motion in an open set. Ann. Appl. Probab. 14 (2004) 1529–1558. [CrossRef] [Google Scholar]
  18. M. D’Ovidio and E. Orsingher, Composition of processes and related partial differential equations. J. Theor. Probab. 24 (2011) 342–375. [CrossRef] [Google Scholar]
  19. W. Ehm, Sample function properties of multi-parameter stable processes. Z. Wahrsch. verw. Geb. 56 (1981) 195–228. [CrossRef] [Google Scholar]
  20. P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton University Press, Princeton (2002). [Google Scholar]
  21. D. Geman and J. Horowitz, Occupation densities. Ann. Probab. 8 (1980) 1–67. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Hahn, K. Kobayashi and S. Umarov, Fokker-Plank-Kolmogorv equations associated with SDEs driven by time-changed fractional Brownian motion. Proc. Amer. Math. Soc. 139 (2011) 691–705. [CrossRef] [MathSciNet] [Google Scholar]
  23. Y. Hu, Hausdorff and packing measures of the level sets of iterated Brownian motion. J. Theoret. Probab. 12 (1999) 313–346. [CrossRef] [MathSciNet] [Google Scholar]
  24. J.P. Kahane, Some Random Series of Functions, 2nd edition. Cambridge University Press (1985). [Google Scholar]
  25. D. Khoshnevisan and Y. Xiao, Images of the Brownian sheet. Trans. Amer. Math. Soc. 359 (2007) 3125–3151. [CrossRef] [MathSciNet] [Google Scholar]
  26. M.A. Lifshits, Gaussian Random Functions. Kluwer Academic Publishers, Dordrecht (1995). [Google Scholar]
  27. W. Linde and Z. Shi, Evaluating the small deviation probabilities for subordinated Lévy processes. Stoch. Process. Appl. 113 (2004) 273–287. [CrossRef] [Google Scholar]
  28. E. Nane, Iterated Brownian motion in parabola-shaped domains. Potential Anal. 24 (2006) 105–123. [CrossRef] [MathSciNet] [Google Scholar]
  29. E. Nane, Iterated Brownian motion in bounded domains in ℝn. Stoch. Process. Appl. 116 (2006) 905–916. [CrossRef] [Google Scholar]
  30. E. Nane, Laws of the iterated logarithm for α-time Brownian motion. Electron. J. Probab. 11 (2006) 434–459. [MathSciNet] [Google Scholar]
  31. E. Nane, Higher order PDE’s and iterated processes. Trans. Amer. Math. Soc. 360 (2008) 2681–2692. [CrossRef] [MathSciNet] [Google Scholar]
  32. E. Nane, Laws of the iterated logarithm for a class of iterated processes. Statist. Probab. Lett. 79 (2009) 1744–1751. [CrossRef] [MathSciNet] [Google Scholar]
  33. E. Orsingher and L. Beghin, Fractional diffusion equations and processes with randomly varying time, Ann. Probab. 37 (2009) 206–249. [CrossRef] [MathSciNet] [Google Scholar]
  34. L.D. Pitt, Local times for Gaussian vector fields. Indiana Univ. Math. J. 27 (1978) 309–330. [CrossRef] [MathSciNet] [Google Scholar]
  35. G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian Random Processes : Stochastic models with infinite variance. Chapman & Hall, New York (1994). [Google Scholar]
  36. K.I. Sato, Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press (1999). [Google Scholar]
  37. A.V. Skorokhod, Asymptotic formulas for stable distribution laws. Selected Translations in Mathematical Statistics and Probability 1 (1961) 157–162; Dokl. Akad. Nauk. SSSR 98 (1954) 731–734. [Google Scholar]
  38. M. Talagrand, Hausdorff measure of trajectories of multiparameter fractional Brownian motion. Ann. Probab. 23 (1995) 767–775. [CrossRef] [MathSciNet] [Google Scholar]
  39. M. Talagrand, Multiple points of trajectories of multiparameter fractional Brownian motion. Probab. Theory Relat. Fields 112 (1998) 545–563. [CrossRef] [Google Scholar]
  40. M.S. Taqqu, Weak Convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 (1975) 287–302. [CrossRef] [Google Scholar]
  41. S.J. Taylor, Sample path properties of a transient stable process. J. Math. Mech. 16 (1967) 1229–1246. [MathSciNet] [Google Scholar]
  42. W. Whitt, Stochastic-Process Limits. Springer, New York (2002). [Google Scholar]
  43. Y. Xiao, Hölder conditions for the local times and Hausdorff measure of the level sets of Gaussian random fields. Probab. Theory Relat. Fields 109 (1997) 129–157. [CrossRef] [Google Scholar]
  44. Y. Xiao, Local times and related properties of multi-dimensional iterated Brownian motion. J. Theoret. Probab. 11 (1998) 383–408. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.