Open Access
Volume 25, 2021
Page(s) 220 - 257
Published online 28 May 2021
  1. P. Abry, P. Flandrin, M.S. Taqqu and D. Veitch, Self-similarity and long range dependence through the wavelet lens. Long-range dependence: Theory and Applications, edited by P. Doukhan, G. Oppenheim, M.S. Taqqu. Birhäuser (2003). [Google Scholar]
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  3. R. Balan and C.A. Tudor, Stochastic heat equation with multiplicative fractional-colored noise. J. Theor. Probab. 23 (2010) 834–870. [Google Scholar]
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  7. J.-M. Bardet and C.A. Tudor, A wavelet analysis of the Rosenblatt process: chaos expansion and estimation of the self-similarity parameter. Stoch. Process. Appl. 120 (2010) 2331–2362. [Google Scholar]
  8. I. Cialenco, Statistical inference for SPDEs: an overview. Stat. Inference Stoch. Process. 21 (2018) 309–329. [Google Scholar]
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  12. M. Khalil and C.A. Tudor, Correlation structure, quadratic variations and parameter estimation for the solution to the wave equation with fractional noise. Electr. J. Stat. 12 (2018) 3639–3672. [Google Scholar]
  13. M. Kleptsyna and A. Le Breton, Statistical analysis of the fractional Ornstein-Uhlenbeck type process. Stat. Inference Stoch. Processes 5 (2002) 229–241. [Google Scholar]
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  19. PTG. Peccati and C.A. Tudor, Gaussian limits for vector-valued multiple stochastic integrals. Séminaire de Probabilités XXXIV (2004) 247–262. [Google Scholar]
  20. B.L.S. Praksa Rao, Semimartingales and their Statistical Inference. Chapman and Hall (1999). [Google Scholar]
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  22. R. Shevchenko, M. Slaoui and C.A. Tudor, Generalized k-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus. J. Statist. Plann. Inference 207 (2020) 155–180. [Google Scholar]
  23. S. Torres, C.A. Tudor and F. Viens, Quadratic variations for the fractional-colored stochastic heat equation. Electr. J. Probab. 19 (2014) 76. [Google Scholar]
  24. C.A. Tudor, Analysis of variations for self-similar processes. A stochastic calculus approach. Probability and its Applications (New York). Springer, Cham (2013). [Google Scholar]
  25. C.A. Tudor and F.G. Viens, Statistical aspects of the fractional stochastic calculus. Ann. Statist. 35 (2007) 1183–1212. [Google Scholar]

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