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References

  • Anh, V. V.; Leonenko, N. N. Scaling laws for fractional diffusion-wave equations with singular data. Statist. Probab. Lett. 48 (2000), no. 3, 239--252. MR1765748
  • Anh, V. V.; Leonenko, N. N. Spectral analysis of fractional kinetic equations with random data. J. Statist. Phys. 104 (2001), no. 5-6, 1349--1387. MR1859007
  • Anh, V. V.; Leonenko, N. N. Spectral theory of renormalized fractional random fields. Teor. Ĭmovīr. Mat. Stat. No. 66 (2002), 3--14; translation in Theory Probab. Math. Statist. No. 66 (2003), 1--13 MR1931155
  • Agrawal, Om P. A general solution for the fourth-order fractional diffusion-wave equation. Fract. Calc. Appl. Anal. 3 (2000), no. 1, 1--12. MR1743402
  • Angulo, J. M.; Ruiz-Medina, M. D.; Anh, V. V.; Grecksch, W. Fractional diffusion and fractional heat equation. Adv. in Appl. Probab. 32 (2000), no. 4, 1077--1099. MR1808915
  • Beghin, Luisa; Orsingher, Enzo. The telegraph process stopped at stable-distributed times and its connection with the fractional telegraph equation. Fract. Calc. Appl. Anal. 6 (2003), no. 2, 187--204. MR2035414
  • Beghin, L.; Orsingher, E. The distribution of the local time for "pseudoprocesses'' and its connection with fractional diffusion equations. Stochastic Process. Appl. 115 (2005), no. 6, 1017--1040. MR2138812
  • Beghin, L.; Orsingher, E.; Ragozina, T. Joint distributions of the maximum and the process for higher-order diffusions. Stochastic Process. Appl. 94 (2001), no. 1, 71--93. MR1835846
  • Beghin, Luisa; Hochberg, Kenneth J.; Orsingher, Enzo. Conditional maximal distributions of processes related to higher-order heat-type equations. Stochastic Process. Appl. 85 (2000), no. 2, 209--223. MR1731022
  • Bingham, N. H. Maxima of sums of random variables and suprema of stable processes. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 26 (1973), 273--296. MR0415780
  • textquotedblleft Integration in function spacestextquotedblright , In: phProgress in Mathematics, R.V. Gamkrelidze, ed., 4, 87-132.
  • textquotedblleft Generalized measures in function spacestextquotedblright , phTheory Prob. Appl., 10, (2) 304-316.
  • , textquotedblleft Pseudoprocessi governati da equazioni frazionarie di ordine superiore al secondotextquotedblright , phTesi di Laurea, Università di Roma textquotedblleft La Sapienzatextquotedblright .
  • Fujita, Yasuhiro. Integrodifferential equation which interpolates the heat equation and the wave equation. Osaka J. Math. 27 (1990), no. 2, 309--321. MR1066629
  • ph, Tables of Integrals, Series and Products, Alan Jeffrey Editor, Academic Press, London.
  • Hochberg, Kenneth J.; Orsingher, Enzo. The arc-sine law and its analogs for processes governed by signed and complex measures. Stochastic Process. Appl. 52 (1994), no. 2, 273-292. MR1290699
  • Hochberg, Kenneth J.; Orsingher, Enzo. Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations. J. Theoret. Probab. 9 (1996), no. 2, 511--532. MR1385409
  • ''Some properties of the distribution corresponding to the equation fracpartial upartial t% =(-1)^p+1fracpartial ^2pupartial x^2p'', phSoviet Math. Dokl., 1, 260-263.
  • Lachal, Aimé. Distributions of sojourn time, maximum and minimum for pseudo-processes governed by higher-order heat-type equations. Electron. J. Probab. 8 (2003), no. 20, 53 pp. (electronic). MR2041821
  • Lachal, Aimé. First hitting time and place for pseudo-processes driven by the equation $\frac\partial{\partial t}=\pm\frac{\partial^ N}{\partial x^ N}$ subject to a linear drift. Stochastic Process. Appl. 118 (2008), no. 1, 1--27. MR2376250
  • Mainardi, Francesco. Fractional relaxation-oscillation and fractional diffusion-wave phenomena. Chaos Solitons Fractals 7 (1996), no. 9, 1461--1477. MR1409912
  • , ''The realization of the generalized transfer equation in a medium with fractal geometry'', ph% Phys. Stat. Sol., (b) 133, 425-430.
  • Nikitin, Y.; Orsingher, E. On sojourn distributions of processes related to some higher-order heat-type equations. J. Theoret. Probab. 13 (2000), no. 4, 997--1012. MR1820499
  • Nishioka, Kunio. The first hitting time and place of a half-line by a biharmonic pseudo process. Japan. J. Math. (N.S.) 23 (1997), no. 2, 235--280. MR1486514
  • ''Processes governed by signed measures connected with third-order 'heat-type' equations'', phLith. Math. Journ., 31, 321-334.
  • ''Time-fractional equations and telegraph processes with Brownian time'', phProbability Theory and Related Fields., 128, 141-160.
  • Podlubny, Igor. Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. Mathematics in Science and Engineering, 198. Academic Press, Inc., San Diego, CA, 1999. xxiv+340 pp. ISBN: 0-12-558840-2 MR1658022
  • Saichev, Alexander I.; Zaslavsky, George M. Fractional kinetic equations: solutions and applications. Chaos 7 (1997), no. 4, 753--764. MR1604710
  • 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
  • , phStable Non-Gaussian Random Processes, Chapman and Hall, New York.
  • Schneider, W. R.; Wyss, W. Fractional diffusion and wave equations. J. Math. Phys. 30 (1989), no. 1, 134--144. MR0974464
  • Wyss, Walter. The fractional Black-Scholes equation. Fract. Calc. Appl. Anal. 3 (2000), no. 1, 51--61. MR1743405


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