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References

  1. O.E. Barndorff-Nielsen, S.E. Graversen and N. Shepard (2004). Power variation and stochastic volatility: a review and some new results. J. Appl. Probab. 44(A), 133-143. MR2057570 (2005e:60145)

  2. K. Burdzy (1993). Some path properties of iterated Brownian motion. In: Seminar on Stochastic Processes (E. Cinlar, K.L. Chung and M.J. Sharpe, eds.), Birkhäuser, Boston, 67-87. MR1278077 (95c:60075)

  3. K. Burdzy (1994). Variation of iterated Brownian motion. In: Measure-Valued Processes, Stochastic Partial Differential Equations and Interacting Systems (D.A. Dawson, ed.), CRM Proceedings and Lecture Notes 5, 35-53. MR1278281 (95h:60123)

  4. K. Burdzy and D. Khoshnevisan (1998). Brownian motion in a Brownian crack. Ann. Appl. Probab 8, 708-748. MR1627764 (99g:60147)

  5. J.M. Corcuera, D. Nualart and J.H.C. Woerner (2006). Power variation of some integral long memory process. Bernoulli 12(4), 713-735. MR2248234 (2008e:60160)

  6. R.D. DeBlassie (2004). Iterated Brownian motion in an open set. Ann. Appl. Probab. 14(3), 1529-1558. MR2071433 (2005f:60172)

  7. T.E. Harris (1965). Diffusions with collisions between particles. J. Appl. Probab. 2, 323-338. MR0184277 (32 #1750)

  8. J. Jacod (1994). Limit of random measures associated with the increments of a Brownian semimartingale. Prépublication de l'Université Paris VI. Math. Review number not available.

  9. J. Jacod and A.N. Shiryayev (1987). Limit Theorems for Stochastic Processes. Springer-Verlag, Berlin, Heidelberg, New York. MR0959133 (89k:60044)

  10. H. Kesten and F. Spitzer (1979). A limit theorem related to a new class of self-similar process. Z. Wahrsch. Verw. Gebiete 50, 5-25. MR0550121 (82a:60149)

  11. D. Khoshnevisan and T.M. Lewis (1999). Stochastic calculus for Brownian motion on a Brownian fracture. Ann. Appl. Probab. 9(3), 629-667. MR1722276 (2001m:60128)

  12. D. Khoshnevisan and T.M. Lewis (1999). Iterated Brownian motion and its intrinsic skeletal structure. In: Progresses in Probability 45, 201-210. Birkhäuser. MR1712242 (2001m:60183)

  13. E. Nane (2006). Iterated Brownian motion in bounded domains in R^n. Stochastic Process. Appl. 116 (6), 905-916. MR2254664 (2007j:60133)

  14. E. Nane (2007). Lifetime asymptotics of iterated Brownian motion in R^n. ESAIM Probab. Stat. 11, 147-160. MR2299652 (2008a:60207)

  15. I. Nourdin (2008). Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion. Ann. Probab., to appear. Math. Review number not available.

  16. I. Nourdin, D. Nualart and C.A. Tudor (2007). Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Prépublication de l'Université Paris VI. Math. Review number not available.

  17. I. Nourdin and A. Réveillac (2008). Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case H=1/4. Prépublication de l'Université Paris VI. Math. Review number not available.

  18. D. Nualart (2006). The Malliavin calculus and related topics. Springer-Verlag, Berlin, 2nd edition. MR2200233 (2006j:60004)

  19. E. Orsingher and L. Beghin (2008). Fractional diffusion equations and processes with randomly-varying time. Ann. Probab., to appear. Math. Review number not available.

  20. G. Peccati and C.A. Tudor (2005). Gaussian limits for vector-valued multiple stochastic integrals. In: Séminaire de Probabilités XXXVIII, 247-262. Lecture Notes in Math. 1857, Springer-Verlag, Berlin. MR2126978 (2006i:60071)

  21. J. Swanson (2007). Variations of the solution to a stochastic heat equation. Ann. Probab. 35, no. 6, 2122-2159. MR2353385

  22. M.S. Taqqu (1975). Weak convergence to fractional Brownian motion and to Rosenblatt process. Z. Wahrsch. Verw. Gebiete 31, 287-302. MR0400329 (53 #4164)



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