Download this PDF file Fullscreen Fullscreen Off
References
- Adler, Robert J. The geometry of random fields. Wiley Series in Probability and Mathematical Statistics. John Wiley & Sons, Ltd., Chichester, 1981. xi+280 pp. ISBN: 0-471-27844-0 MR0611857
- Adler, Robert J.; Taylor, Jonathan E. Random fields and geometry. Springer Monographs in Mathematics. Springer, New York, 2007. xviii+448 pp. ISBN: 978-0-387-48112-8 MR2319516
- Applebaum, David. Lévy processes and stochastic calculus. Second edition. Cambridge Studies in Advanced Mathematics, 116. Cambridge University Press, Cambridge, 2009. xxx+460 pp. ISBN: 978-0-521-73865-1 MR2512800
- Arneodo, Alain; Bacry, Emmanuel; Jaffard, Stéphane; Muzy, Jean François Oscillating singularities on Cantor sets: a grand-canonical multifractal formalism. J. Statist. Phys. 87 (1997), no. 1-2, 179--209. MR1453739
- Arneodo, Alain; Bacry, Emmanuel; Jaffard, Stéphane; Muzy, Jean François Singularity spectrum of multifractal functions involving oscillating singularities. J. Fourier Anal. Appl. 4 (1998), no. 2, 159--174. MR1650933
- Ayache, Antoine and Hamonier, Julien. Linear Multifractional Stable Motion: fine path properties. phPreprint, 2013.
- Ayache, Antoine; Taqqu, Murad S. Multifractional processes with random exponent. Publ. Mat. 49 (2005), no. 2, 459--486. MR2177638
- Ayache, Antoine; Roueff, François; Xiao, Yimin. Linear fractional stable sheets: wavelet expansion and sample path properties. Stochastic Process. Appl. 119 (2009), no. 4, 1168--1197. MR2508569
- Balança, Paul. Some sample path properties of multifractional brownian motion. Preprint, 2014.
- Barral, Julien; Seuret, Stéphane. The singularity spectrum of Lévy processes in multifractal time. Adv. Math. 214 (2007), no. 1, 437--468. MR2348038
- Barral, Julien; Seuret, Stéphane. A localized Jarník-Besicovitch theorem. Adv. Math. 226 (2011), no. 4, 3191--3215. MR2764886
- Barral, Julien; Fournier, Nicolas; Jaffard, Stéphane; Seuret, Stéphane. A pure jump Markov process with a random singularity spectrum. Ann. Probab. 38 (2010), no. 5, 1924--1946. MR2722790
- Benassi, Albert; Cohen, Serge; Istas, Jacques. On roughness indices for fractional fields. Bernoulli 10 (2004), no. 2, 357--373. MR2046778
- Blumenthal, Robert M.; Getoor, Ronald K. Sample functions of stochastic processes with stationary independent increments. J. Math. Mech. 10 1961 493--516. MR0123362
- Bony, Jean-Michel. Second microlocalization and propagation of singularities for semilinear hyperbolic equations. Hyperbolic equations and related topics (Katata/Kyoto, 1984), 11--49, Academic Press, Boston, MA, 1986. MR0925240
- Cohen, Serge; Lacaux, Céline; Ledoux, Michel. A general framework for simulation of fractional fields. Stochastic Process. Appl. 118 (2008), no. 9, 1489--1517. MR2442368
- Dozzi, Marco; Shevchenko, Georgiy. Real harmonizable multifractional stable process and its local properties. Stochastic Process. Appl. 121 (2011), no. 7, 1509--1523. MR2802463
- Durand, Arnaud. Random wavelet series based on a tree-indexed Markov chain. Comm. Math. Phys. 283 (2008), no. 2, 451--477. MR2430640
- Durand, Arnaud. Singularity sets of Lévy processes. Probab. Theory Related Fields 143 (2009), no. 3-4, 517--544. MR2475671
- Durand, Arnaud; Jaffard, Stéphane. Multifractal analysis of Lévy fields. Probab. Theory Related Fields 153 (2012), no. 1-2, 45--96. MR2925570
- A. Echelard. Analyse 2-microlocale et application au débruitage. PhD thesis, Université de Nantes, 2007. http://tel.archives-ouvertes.fr/tel-00283008/fr/.
- Falconer, Kenneth J. The geometry of fractal sets. Cambridge Tracts in Mathematics, 85. Cambridge University Press, Cambridge, 1986. xiv+162 pp. ISBN: 0-521-25694-1; 0-521-33705-4 MR0867284
- Falconer, Kenneth J. Fractal geometry. Mathematical foundations and applications. Second edition. John Wiley & Sons, Inc., Hoboken, NJ, 2003. xxviii+337 pp. ISBN: 0-470-84861-8 MR2118797
- Herbin, Erick; Lévy Véhel, Jacques. Stochastic 2-microlocal analysis. Stochastic Process. Appl. 119 (2009), no. 7, 2277--2311. MR2531092
- Jaffard, Stéphane Pointwise smoothness, two-microlocalization and wavelet coefficients. Conference on Mathematical Analysis (El Escorial, 1989). Publ. Mat. 35 (1991), no. 1, 155--168. MR1103613
- Jaffard, Stéphane. The multifractal nature of Lévy processes. Probab. Theory Related Fields 114 (1999), no. 2, 207--227. MR1701520
- Jaffard, Stéphane; Meyer, Yves. Wavelet methods for pointwise regularity and local oscillations of functions. Mem. Amer. Math. Soc. 123 (1996), no. 587, x+110 pp. MR1342019
- Jaffard, Stéphane; Meyer, Yves. On the pointwise regularity of functions in critical Besov spaces. J. Funct. Anal. 175 (2000), no. 2, 415--434. MR1780484
- Khoshnevisan, Davar; Shi, Zhan. Fast sets and points for fractional Brownian motion. Séminaire de Probabilités, XXXIV, 393--416, Lecture Notes in Math., 1729, Springer, Berlin, 2000. MR1768077
- Khoshnevisan, Davar; Xiao, Yimin. Level sets of additive Lévy processes. Ann. Probab. 30 (2002), no. 1, 62--100. MR1894101
- Khoshnevisan, Davar; Shieh, Narn-Rueih; Xiao, Yimin. Hausdorff dimension of the contours of symmetric additive Lévy processes. Probab. Theory Related Fields 140 (2008), no. 1-2, 129--167. MR2357673
- Kolwankar, Kiran M.; Lévy Véhel, Jacques. A time domain characterization of the fine local regularity of functions. J. Fourier Anal. Appl. 8 (2002), no. 4, 319--334. MR1912634
- Kono, Norio; Maejima, Makoto. Hölder continuity of sample paths of some self-similar stable processes. Tokyo J. Math. 14 (1991), no. 1, 93--100. MR1108158
- Lévy Véhel, Jacques; Seuret, Stéphane. The 2-microlocal formalism. Fractal geometry and applications: a jubilee of Benoît Mandelbrot, Part 2, 153--215, Proc. Sympos. Pure Math., 72, Part 2, Amer. Math. Soc., Providence, RI, 2004. MR2112123
- Maejima, Makoto. A self-similar process with nowhere bounded sample paths. Z. Wahrsch. Verw. Gebiete 65 (1983), no. 1, 115--119. MR0717937
- Marcus, Michael B.; Rosen, Jay. Markov processes, Gaussian processes, and local times. Cambridge Studies in Advanced Mathematics, 100. Cambridge University Press, Cambridge, 2006. x+620 pp. ISBN: 978-0-521-86300-1; 0-521-86300-7 MR2250510
- Marquardt, Tina. Fractional Lévy processes with an application to long memory moving average processes. Bernoulli 12 (2006), no. 6, 1099--1126. MR2274856
- Meyer, Yves. Wavelets, vibrations and scalings. With a preface in French by the author. CRM Monograph Series, 9. American Mathematical Society, Providence, RI, 1998. x+133 pp. ISBN: 0-8218-0685-8 MR1483896
- Orey, Steven; Taylor, S. James. How often on a Brownian path does the law of iterated logarithm fail? Proc. London Math. Soc. (3) 28 (1974), 174--192. MR0359031
- Perkins, Edwin. On the Hausdorff dimension of the Brownian slow points. Z. Wahrsch. Verw. Gebiete 64 (1983), no. 3, 369--399. MR0716493
- Picard, Jean. Representation formulae for the fractional Brownian motion. Séminaire de Probabilités XLIII, 3--70, Lecture Notes in Math., 2006, Springer, Berlin, 2011. MR2790367
- Pruitt, William E. The growth of random walks and Lévy processes. Ann. Probab. 9 (1981), no. 6, 948--956. MR0632968
- Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357
- Samko, Stefan G.; Kilbas, Anatoly A.; Marichev, Oleg I. Fractional integrals and derivatives. Theory and applications. Edited and with a foreword by S. M. Nikolʹskiĭ. Translated from the 1987 Russian original. Revised by the authors. Gordon and Breach Science Publishers, Yverdon, 1993. xxxvi+976 pp. ISBN: 2-88124-864-0 MR1347689
- Samorodnitsky, Gennady; Taqqu, Murad S. Stable non-Gaussian random processes. Stochastic models with infinite variance. Stochastic Modeling. Chapman & Hall, New York, 1994. xxii+632 pp. ISBN: 0-412-05171-0 MR1280932
- Sato, Ken-iti. Lévy processes and infinitely divisible distributions. Translated from the 1990 Japanese original. Revised by the author. Cambridge Studies in Advanced Mathematics, 68. Cambridge University Press, Cambridge, 1999. xii+486 pp. ISBN: 0-521-55302-4 MR1739520
- Seuret, Stéphane and Lévy~Véhel, Jacques. The local Hölder function of a continuous function. phAppl. Comput. Harmon. Anal., 13penalty0 (3):penalty0 263--276, 2002. MR1942744
- Seuret, Stéphane; Lévy Véhel, Jacques. A time domain characterization of 2-microlocal spaces. J. Fourier Anal. Appl. 9 (2003), no. 5, 473--495. MR2027889
- Stoev, Stilian; Taqqu, Murad S. Stochastic properties of the linear multifractional stable motion. Adv. in Appl. Probab. 36 (2004), no. 4, 1085--1115. MR2119856
- Stoev, Stilian; Taqqu, Murad S. Path properties of the linear multifractional stable motion. Fractals 13 (2005), no. 2, 157--178. MR2151096
- Takashima, Keizo. Sample path properties of ergodic self-similar processes. Osaka J. Math. 26 (1989), no. 1, 159--189. MR0991287
- Xiao, Yimin. Uniform modulus of continuity of random fields. Monatsh. Math. 159 (2010), no. 1-2, 163--184. MR2564392
This work is licensed under a Creative Commons Attribution 3.0 License.