Characterization and analysis of generalized grey incomplete gamma noise

References

• S. Albeverio, Y. Daletzky, Y.G. Kondratiev, and L. Streit, Non-Gaussian infinite dimensional analysis, J. Funct. Anal. 138 (1996), pp. 311–350.
   Web of Science ®Google Scholar
• G. Ascione, Abstract Cauchy problems for the generalized fractional calculus, Nonlinear Anal. 209 (2021), pp. 112339.
   Web of Science ®Google Scholar
• D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo, Fractional Calculus: Models and Numerical Methods. Vol. 3. World Scientific, Singapore, 2012.
   Google Scholar
• L. Beghin and J. Gajda, Tempered relaxation equation and related generalized stable processes, Fract. Calc. Appl. Anal. 23(5) (2020), pp. 1248–1273.
   Web of Science ®Google Scholar
• L. Beghin, L. Cristofaro, and J. Gajda, Non-Gaussian Measures in Infinite Dimensional Spaces: the Gamma-Grey Noise. arXiv preprint arXiv:2207.13609, 2022.
   Google Scholar
• L. Beghin, L. Cristofaro, and Y. Mishura, A class of infinite-dimensional Gaussian processes defined through generalized fractional operators. arXiv preprint arXiv:2309.13283. (2023).
   Google Scholar
• W. Bock and J.L. Da Silva, Wick type SDEs driven by grey Brownian motion, in AIP Conference Proceedings. AIP Publishing LLC, 2017, pp. 020004.
   Google Scholar
• W. Bock, S. Desmettre, and J.L. Da Silva, Integral representation of generalized grey Brownian motion, Stochastics 92(4) (2020), pp. 552–565.
   Web of Science ®Google Scholar
• R. Capitanelli and M. D'Ovidio, Fractional Cauchy problem on random snowflakes, J. Evol. Equ.21(2) (2021), pp. 2123–2140.
   Web of Science ®Google Scholar
• J.L. Da Silva, M. Erraoui, and H. Ouerdiane, Generalized fractional evolution equation, Fract. Calc. Appl. Anal. 10(4) (2007), pp. 375–398.
   Google Scholar
• G. Di Nunno and B. Øksendal, The Donsker delta function, a representation formula for functionals of a Lévy process and application to hedging in incomplete markets, Sémin. Congr. Soc. Math. France 16(1) (2004), pp. 71–82.
   Google Scholar
• M. Grothaus and F. Jahnert, Mittag-Leffler analysis II: Application to the fractional heat equation, J. Funct. Anal. 270(7) (2016), pp. 2732–2768.
   Web of Science ®Google Scholar
• M. Grothaus, F. Jahnert, F. Riemann, and J.L. da Silva, Mittag–Leffler analysis I: Construction and characterization, J. Funct. Anal. 268(7) (2015), pp. 1876–1903.
   Web of Science ®Google Scholar
• M. Grothaus, J. Müller, and A. Nonnenmacher, An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs, Stoch. Partial Differ. Equ. Anal. Comput. 10(2) (2022), pp. 359–391.
   Web of Science ®Google Scholar
• R.Y. Hachemi and B. Øksendal, The time-fractional stochastic heat equation driven by time-space white noise. arXiv preprint arXiv:2211.12861. 2022 Nov 23.
   Google Scholar
• T. Hida, H.H. Kuo, J. Potthoff, and L. Streit, White Noise: An Infinite Dimensional Calculus. Vol. 253. Springer Science & Business Media, Dordrecht, 1993.
   Google Scholar
• T. Hida and L. Streit, Let Us Use White Noise, World Scientific, Singapore, 2017.
   Google Scholar
• Y. Hu and B. Øksendal, Fractional white noise calculus and applications to finance, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 6(1) (2003), pp. 1–32.
   Web of Science ®Google Scholar
• Y. Ito, Generalized poisson functionals, Prob. Th. Rel. Fields 77(1) (1988), pp. 1–28.
   Web of Science ®Google Scholar
• D. Karp and E. Prilepkina, Hypergeometric functions as generalized Stieltjes transforms, J. Math. Anal. Appl. 393(2) (2012), pp. 348–359.
   Web of Science ®Google Scholar
• A.A. Kilbas and M. Saigo, H-transforms: Theory and Applications, CRC Press, Boca Raton, FL, 2004.
   Google Scholar
• Y.G. Kondratiev, P. Leukert, J. Potthoff, L. Streit, and W. Westerkamp, Generalized functionals in Gaussian spaces: The characterization theorem revisited, J. Funct. Anal. 141(2) (1996), pp. 301–318.
   Web of Science ®Google Scholar
• Y.G. Kondratiev, J.L. da Silva, L. Streit, and G.F. Us, Analysis on Poisson and gamma spaces, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 1(1) (1998), pp. 91–117.
   Web of Science ®Google Scholar
• Y.G. Kondratiev, L. Streit, W. Westerkamp, and J.A. Yan, Generalized functions in infinite-dimensional analysis, Hiroshima Math. J. 28(2) (1998), pp. 213–260.
   Google Scholar
• H.-H. Kuo, White Noise Distribution Theory, CRC Press, Boca Raton, New York, London and Tokyo, 1996.
   Google Scholar
• A.M. Mathai, R.K. Saxena, and H.J. Haubold, The H-function: Theory and Applications, Springer Science and Business Media, New York, 2009.
   Google Scholar
• Y.S. Mishura, Stochastic Calculus for Fractional Brownian Motion and Related Processes, volume 1929 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2008.
   Google Scholar
• A. Mura and G. Pagnini, Characterizations and simulations of a class of stochastic processes to model anomalous diffusion, J. Phys. A. 41(28) (2008), pp. 285003.
   Google Scholar
• N. Obata, White Noise Calculus and Fock Space, Volume 1577 of Lecture Notes in Math, Springer-Verlag, Berlin, Heidelberg and New York, 1994.
   Google Scholar
• B. Øksendal and F. Proske, White noise of Poisson random measures, Potential Anal. 21 (2004), pp. 375–403.
   Web of Science ®Google Scholar
• F.W. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark, and A.B.O. Dalhuis, Digital library of mathematical functions, National Institute of Standards and Technology from http://dlmf. nist. gov/(release date 2011-07-01), Washington, DC, 2010.
   Google Scholar
• G. Pagnini, Erdélyi–Kober fractional diffusion, Fract. Calc. Appl. Anal. 15 (2012), pp. 117–127.
   Web of Science ®Google Scholar
• J. Potthoff and L. Streit, A characterization of Hida distributions, J. Funct. Anal. 101 (1991), pp. 212–229.
   Web of Science ®Google Scholar
• A.P. Prudnikov, Y.A. Brychkov, and O.I. Marichev, Integrals and Series: Direct Laplace Transforms, Vol. CRC, Boca Raton, 4. 1982. 0018–9251.
   Google Scholar
• S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional Integrals and Derivatives, Vol. 1. Gordon and breach science publishers, Yverdon, Yverdon-les-Bains, Switzerland, 1993.
   Google Scholar
• R.L. Schilling, R. Song, and Z. Vondracek, Bernstein functions, in Bernstein functions. de Gruyter, 2012.
   Google Scholar
• W.R. Schneider, Grey noise, Stoch. Process. Phys. Geometry 5 (1988), pp. 676–681.
   Google Scholar
• B. Toaldo, Convolution-type derivatives, hitting-times of subordinators and time-changed C 0-semigroups, Potential Anal. 42 (2015), pp. 115–140.
   Web of Science ®Google Scholar