Free Access
Issue
ESAIM: PS
Volume 16, 2012
Page(s) 1 - 24
DOI https://doi.org/10.1051/ps/2011103
Published online 09 March 2012
  1. R.J. Adler, The Geometry of Random Fields. Wiley, New York (1981).
  2. H. Allouba and W. Zheng, Brownian-time processes : the pde connection and the half-derivative generator. Ann. Probab. 29 (2001) 1780–1795. [CrossRef]
  3. F. Aurzada and M. Lifshits, On the Small deviation problem for some iterated processes. Electron. J. Probab. 14 (2009) 1992–2010.
  4. B. Baeumer, M.M. Meerschaert and E. Nane, Brownian subordinators and fractional Cauchy problems. Trans. Amer. Math. Soc. 361 (2009) 3915–3930. [CrossRef]
  5. B. Baeumer, M.M. Meerschaert and E. Nane, Space-time duality for fractional diffusion. J. Appl. Probab. 46 (2009) 1100–1115. [CrossRef]
  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]
  7. S.M. Berman, Local times and sample function properties of stationary Gaussian processes. Trans. Amer. Math. Soc. 137 (1969) 277–299. [CrossRef] [MathSciNet]
  8. S.M. Berman, Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J. 23 (1973) 69–94. [CrossRef]
  9. J. Bertoin, Lévy Processes. Cambridge University Press (1996).
  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.
  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.
  12. K. Burdzy and D. Khoshnevisan, Brownian motion in a Brownian crack. Ann. Appl. Probab. 8 (1998) 708–748. [CrossRef]
  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]
  14. J. Cuzick and J. DuPreez, Joint continuity of Gaussian local times. Ann. Probab. 10 (1982) 810–817. [CrossRef]
  15. Y. Davydov, The invariance principle for stationary processes. Teor. Verojatnost. i Primenen. 15 (1970) 498–509.
  16. R.D. DeBlassie, Higher order PDE’s and symmetric stable processes. Probab. Theory Relat. Fields 129 (2004) 495–536.
  17. R.D. DeBlassie, Iterated Brownian motion in an open set. Ann. Appl. Probab. 14 (2004) 1529–1558. [CrossRef]
  18. M. D’Ovidio and E. Orsingher, Composition of processes and related partial differential equations. J. Theor. Probab. 24 (2011) 342–375. [CrossRef]
  19. W. Ehm, Sample function properties of multi-parameter stable processes. Z. Wahrsch. verw. Geb. 56 (1981) 195–228. [CrossRef]
  20. P. Embrechts and M. Maejima, Selfsimilar Processes. Princeton University Press, Princeton (2002).
  21. D. Geman and J. Horowitz, Occupation densities. Ann. Probab. 8 (1980) 1–67. [CrossRef] [MathSciNet]
  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]
  23. Y. Hu, Hausdorff and packing measures of the level sets of iterated Brownian motion. J. Theoret. Probab. 12 (1999) 313–346. [CrossRef] [MathSciNet]
  24. J.P. Kahane, Some Random Series of Functions, 2nd edition. Cambridge University Press (1985).
  25. D. Khoshnevisan and Y. Xiao, Images of the Brownian sheet. Trans. Amer. Math. Soc. 359 (2007) 3125–3151. [CrossRef] [MathSciNet]
  26. M.A. Lifshits, Gaussian Random Functions. Kluwer Academic Publishers, Dordrecht (1995).
  27. W. Linde and Z. Shi, Evaluating the small deviation probabilities for subordinated Lévy processes. Stoch. Process. Appl. 113 (2004) 273–287. [CrossRef]
  28. E. Nane, Iterated Brownian motion in parabola-shaped domains. Potential Anal. 24 (2006) 105–123. [CrossRef] [MathSciNet]
  29. E. Nane, Iterated Brownian motion in bounded domains in ℝn. Stoch. Process. Appl. 116 (2006) 905–916. [CrossRef]
  30. E. Nane, Laws of the iterated logarithm for α-time Brownian motion. Electron. J. Probab. 11 (2006) 434–459. [MathSciNet]
  31. E. Nane, Higher order PDE’s and iterated processes. Trans. Amer. Math. Soc. 360 (2008) 2681–2692. [CrossRef] [MathSciNet]
  32. E. Nane, Laws of the iterated logarithm for a class of iterated processes. Statist. Probab. Lett. 79 (2009) 1744–1751. [CrossRef] [MathSciNet]
  33. E. Orsingher and L. Beghin, Fractional diffusion equations and processes with randomly varying time, Ann. Probab. 37 (2009) 206–249. [CrossRef] [MathSciNet]
  34. L.D. Pitt, Local times for Gaussian vector fields. Indiana Univ. Math. J. 27 (1978) 309–330. [CrossRef] [MathSciNet]
  35. G. Samorodnitsky and M.S. Taqqu, Stable non-Gaussian Random Processes : Stochastic models with infinite variance. Chapman & Hall, New York (1994).
  36. K.I. Sato, Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press (1999).
  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.
  38. M. Talagrand, Hausdorff measure of trajectories of multiparameter fractional Brownian motion. Ann. Probab. 23 (1995) 767–775. [CrossRef] [MathSciNet]
  39. M. Talagrand, Multiple points of trajectories of multiparameter fractional Brownian motion. Probab. Theory Relat. Fields 112 (1998) 545–563. [CrossRef]
  40. M.S. Taqqu, Weak Convergence to fractional Brownian motion and to the Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31 (1975) 287–302. [CrossRef]
  41. S.J. Taylor, Sample path properties of a transient stable process. J. Math. Mech. 16 (1967) 1229–1246. [MathSciNet]
  42. W. Whitt, Stochastic-Process Limits. Springer, New York (2002).
  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]
  44. Y. Xiao, Local times and related properties of multi-dimensional iterated Brownian motion. J. Theoret. Probab. 11 (1998) 383–408. [CrossRef] [MathSciNet]

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