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References
- Burdzy, Krzysztof. Some path properties of iterated Brownian motion. Seminar on Stochastic Processes, 1992 (Seattle, WA, 1992), 67--87, Progr. Probab., 33, Birkhäuser Boston, Boston, MA, 1993. MR1278077
- Burdzy, Krzysztof. Variation of iterated Brownian motion. Measure-valued processes, stochastic partial differential equations, and interacting systems (Montreal, PQ, 1992), 35--53, CRM Proc. Lecture Notes, 5, Amer. Math. Soc., Providence, RI, 1994. MR1278281
- Burdzy, Krzysztof; Khoshnevisan, Davar. Brownian motion in a Brownian crack. Ann. Appl. Probab. 8 (1998), no. 3, 708--748. MR1627764
- Burdzy, Krzysztof; Swanson, Jason. A change of variable formula with Itô correction term. Ann. Probab. 38 (2010), no. 5, 1817--1869. MR2722787
- Cheridito, Patrick; Nualart, David. Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter $H\in(0,{1\over2})$. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 6, 1049--1081. MR2172209
- Gradinaru, Mihai; Nourdin, Ivan; Russo, Francesco; Vallois, Pierre. $m$-order integrals and generalised Itô's formula: the case of a fractional Brownian motion with any Hurst index. Ann. Inst. H. Poincaré Probab. Statist. 41 (2005), no. 4, 781--806. MR2144234
- Harnett, Daniel; Nualart, David. Central limit theorem for a Stratonovich integral with Malliavin calculus. Ann. Probab. 41 (2013), no. 4, 2820--2879. MR3112933
- Harnett, Daniel; Nualart, David. Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes. Stochastic Process. Appl. 122 (2012), no. 10, 3460--3505. MR2956113
- Harnett, Daniel; Nualart, David. Central limit theorem for a Stratonovich integral with Malliavin calculus. Ann. Probab. 41 (2013), no. 4, 2820--2879. MR3112933
- Khoshnevisan, Davar; Lewis, Thomas M. Stochastic calculus for Brownian motion on a Brownian fracture. Ann. Appl. Probab. 9 (1999), no. 3, 629--667. MR1722276
- Khoshnevisan, Davar; Lewis, Thomas M. Iterated Brownian motion and its intrinsic skeletal structure. Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), 201--210, Progr. Probab., 45, Birkhäuser, Basel, 1999. MR1712242
- Nourdin, Ivan. A change of variable formula for the 2D fractional Brownian motion of Hurst index bigger or equal to $1/4$. J. Funct. Anal. 256 (2009), no. 7, 2304--2320. MR2498767
- Nourdin, Ivan; Nualart, David; Tudor, Ciprian A. Central and non-central limit theorems for weighted power variations of fractional Brownian motion. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010), no. 4, 1055--1079. MR2744886
- Nourdin, Ivan; Peccati, Giovanni. Weighted power variations of iterated Brownian motion. Electron. J. Probab. 13 (2008), no. 43, 1229--1256. MR2430706
- Nourdin, Ivan; Réveillac, Anthony. Asymptotic behavior of weighted quadratic variations of fractional Brownian motion: the critical case $H=1/4$. Ann. Probab. 37 (2009), no. 6, 2200--2230. MR2573556
- Nourdin, Ivan; Réveillac, Anthony; Swanson, Jason. The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter $1/6$. Electron. J. Probab. 15 (2010), no. 70, 2117--2162. MR2745728
- R. Zeineddine (2013): Fluctuations of the power variation of fractional Brownian motion in Brownian time. Bernoulli, to appear.
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