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References

  • Bassan, Bruno; Bona, Elisabetta. Moments of stochastic processes governed by Poisson random measures. Comment. Math. Univ. Carolin. 31 (1990), no. 2, 337--343. MR1077904
  • Biermé, Hermine; Estrade, Anne; Kaj, Ingemar. Self-similar random fields and rescaled random balls models. J. Theoret. Probab. 23 (2010), no. 4, 1110--1141. MR2735739
  • Breton, Jean-Christophe; Dombry, Clément. Functional macroscopic behavior of weighted random ball model. ALEA Lat. Am. J. Probab. Math. Stat. 8 (2011), 177--196. MR2786559
  • Beghin, L.; Orsingher, E. Fractional Poisson processes and related planar random motions. Electron. J. Probab. 14 (2009), no. 61, 1790--1827. MR2535014
  • Chainais P., phInfinitely Divisible Cascades to Model the Statistics of Natural Images, IEEE Trans. Pattern analysis and Machine intelligence, 29, 12, 2105--2119, (2007).
  • Cioczek-Georges, R.; Mandelbrot, B. B. A class of micropulses and antipersistent fractional Brownian motion. Stochastic Process. Appl. 60 (1995), no. 1, 1--18. MR1362316
  • Cohen, Serge; Taqqu, Murad S. Small and large scale behavior of the Poissonized Telecom process. Methodol. Comput. Appl. Probab. 6 (2004), no. 4, 363--379. MR2108557
  • Guyon, Xavier; León, José. Convergence en loi des $H$-variations d'un processus gaussien stationnaire sur ${\bf R}$. (French) [Convergence in law of the $H$-variations of a stationary Gaussian process in ${\bf R}$] Ann. Inst. H. Poincaré Probab. Statist. 25 (1989), no. 3, 265--282. MR1023952
  • Heinrich, Lothar; Schmidt, Volker. Normal convergence of multidimensional shot noise and rates of this convergence. Adv. in Appl. Probab. 17 (1985), no. 4, 709--730. MR0809427
  • Istas, Jacques; Lang, Gabriel. Quadratic variations and estimation of the local Hölder index of a Gaussian process. Ann. Inst. H. Poincaré Probab. Statist. 33 (1997), no. 4, 407--436. MR1465796
  • Kaj, Ingemar; Leskelä, Lasse; Norros, Ilkka; Schmidt, Volker. Scaling limits for random fields with long-range dependence. Ann. Probab. 35 (2007), no. 2, 528--550. MR2308587
  • Kaj, Ingemar; Taqqu, Murad S. Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In and out of equilibrium. 2, 383--427, Progr. Probab., 60, Birkhäuser, Basel, 2008. MR2477392
  • Peccati, Giovanni; Taqqu, Murad S. Central limit theorems for double Poisson integrals. Bernoulli 14 (2008), no. 3, 791--821. MR2537812
  • Perrin E., Harba R., Jennane R. and Iribarren I. phFast and exact synthesis for 1-D fractional Brownian motion and fractional Gaussian noises, Signal Processing Letters IEEE, Vol.9 (1), 382--384, (2002).
  • Sato, Yumiko. Distributions of stable random fields of Chentsov type. Nagoya Math. J. 123 (1991), 119--139. MR1126186
  • 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
  • Stoyan, D.; Kendall, W. S.; Mecke, J. Stochastic geometry and its applications. With a foreword by D. G. Kendall. Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics. John Wiley & Sons, Ltd., Chichester, 1987. 345 pp. ISBN: 0-471-90519-4 MR0895588
  • Takenaka, Shigeo. Integral-geometric construction of self-similar stable processes. Nagoya Math. J. 123 (1991), 1--12. MR1126180


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