References
- S. Bianchi and A. Pianese, Multifractional processes in finance, (2013). SSRN. Available at https://ssrn.com/abstract=2331509.
- S. Cohen, From self-similarity to local self-similarity: the estimation problem, in Fractals: Theory and Applications in engineering, Springer, 1999.
- S. Corlay, J. Lebovits, and J.L. Véhel, Multifractional stochastic volatility models. Math. Financ. 24 (2014), pp. 364–402. doi:10.1111/mafi.12024.
- M. Gubinelli, Controlling rough paths. arxiv 0306433, 2003.
- M. Hairer and P. Friz, A Course on Rough Paths with an Introduction to Regularity Structures, Springer International Publishing, Cham, Switzerland, 2014.
- E. Herbin, J. Lebovits, and J.L. Vehel, Stochastic integration with respect to multi fractional Brownian motion via tangent fractional Brownian motions. Stochastic processes and their applications, September 2013.
- S.C. Lim, Fractional Brownian motion and multifractional Brownian motion of Rieman–Liouville type, J. Phys. A-Math. Gen. 34 (2001), pp. 1301–1310. doi: 10.1088/0305-4470/34/7/306
- J. Lebovits and J.L. Véhel, White noise-based stochastic calculus with respect to multifractional Brownian motion. Stochastics. 86(1) (2014), 87–124. doi:10.1080/17442508.2012.758727.
- T. Lyons, Differential equations driven by rough signals. Rev. Mat. Iberoam. 14 (1998), pp. 215–310. doi:10.4171/RMI/240.
- R. Marty, B. Boufoussi, and M. Dozzi, Local time and Tanaka formula for a Volterra-type multifractional Gaussian process (2010). Available at doi:https://projecteuclid.org/euclid.bj/1290092907.
- I. Nourdin, A. Neuenkirch, and S. Tindel, Delay equations driven by rough paths, Electron. J. Probab. 13(67) (2008), pp. 2031–2068.
- A. Pianese, S. Bianchi, and A. Pantanella, Modelling stock prices by multi fractional Brownian motion: an improved estimation of the pointless regularity, Quant. Financ. 13(8) (2011), pp. 1317–1330. doi:10.1080/14697688.2011.594080.
- F. Proske, F.A. Harang, and T. Nilssen, Girsanov theorem for multifractional Brownian processes. Arxiv, 2017.
- J. Roux Benassi, Elliptic Gaussian random processes, Rev. Math. Iber. 13(1) (1997), pp. 19–90. doi: 10.4171/RMI/217
- S. Samko, Fractional integration and differentiation of variable order: an overview. Nonlinear Dyn. 71(4) (2013), pp. 653–662. doi:10.1007/s11071-012-0485-0.
- S. Samko and B. Ross, Fractional integration operator of variable order in the Holder spaces H, Internat. J. Math. Math. Sci. 18(4) (1995), pp. 777–788. doi: 10.1155/S0161171295001001
- S. Tindel and D. Nualart, A construction of the rough path above fractional Brownian motion using Volterra representation, Ann. Probab. 39(3) (2011), pp. 1061–1096. doi: 10.1214/10-AOP578
- J.L. Vehel, A. Ayache, and S. Cohen, The covariance structure of multifractional Brownian motion, with application to long range dependence (2011). HAL: id. inria-00581032.
- N. Victoir and P. Friz, Multidimensional Stochastic Processes as Rough Paths, Cambridge Studies in Advanced Mathematics, 2009.
- J.L. Vehel and R.-F. Peltier, Multifractional Brownian motion: definition and preliminary results. HAL Id: inria-0074045, 1995.