Ba, Demba Bocar Fractional operators and applications to fractional martingal. (English) Zbl 1471.60061 Int. J. Adv. Appl. Math. Mech. 5, No. 3, 44-52 (2018). Summary: In this paper, we use the fractional operators for to give the fractional martingale properties. We give again some examples. MSC: 60G46 Martingales and classical analysis 26A33 Fractional derivatives and integrals Keywords:fractional operators; fractional martingales × Cite Format Result Cite Review PDF Full Text: Link References: [1] A.A. Kilbas. H.M.Srivastava, J.J. Trujillo, Theory and Applications of fractional differential equations, NorthHolland mathematics studies, Elsevier, Amsterdam, 204 (2006) · Zbl 1092.45003 [2] S.M. Berman, Local nondeterminism and local times of Gaussian processes, indiana Univ. Math. J. 23 (1973) 6994. · Zbl 0264.60024 [3] M.E. Caballero, B. Fernandez, D. Nualart, Estimation of densities and applications, J. Theoret.Probab.11(3) (1998) 831-851. · Zbl 0953.62081 [4] V.H. De la P˜ena, A general class of exponential inequalities for martingales and ratios, Anna. Probab. 27(1) (1999) 537-564. · Zbl 0942.60004 [5] A.M. Garcia, E. Rodemich, H. Rumsey jr., A real variable lemma and the continuity of paths of some Gaussian processes, indiana Univ. Math. J. 20 (1970) 565-578. · Zbl 0252.60020 [6] D. German, J. Horowitz, Occupations densities, Ann. Probab.8(1) (1980) 1-67. · Zbl 0499.60081 [7] Y. Hu, D. Nualart, J. Song, Fractional martingales and characterization of the fractional Brownian motion, Ann. Probab. 37(6) (2009) 2404-2430. · Zbl 1196.60075 [8] R. Liptser, V. Spokoiny, Deviation probability bound for martingales with applications to statistical estimation, Statist. Probab. Lett. 46(4) (2000) 347-357. · Zbl 0953.62080 [9] D. Nualart, The Malliavin Calculus and related Topics,. second ed. In: Probability and its Applications (New York), Springer-Verlag, Berlin, 2006. · Zbl 1099.60003 [10] D. Nualart, C. Rovira, Large deviations for stochastic Volterra equations, Bernouilli 6(2) (2000) 339-355. · Zbl 0959.60050 [11] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion. third ed. In: Grundlehren der Mathematischen Wissenschaften(Fundamental Principles of Mathematical Sciences), Vol. 293, Springer-Verlag, Berlin, 1999. · Zbl 0917.60006 [12] C. Rovira, M. Sanz-sol é, The law of the solution to a nonlinear hyperbolic SPDE , J. Theoret. Probab. 9(4) (1996) 863-901. · Zbl 0878.60040 [13] B. Saussereau, Non parametric inference for fractional diffusion,ArXiv:1111.0446, 2011. · Zbl 1400.62069 [14] R.B. Sowers, Large deviations for a reaction-diffusion equation with non-Gaussian perturbations, Ann. Probab. 20(1) (1992) 504-537. · Zbl 0749.60059 [15] R. Durrett, Probability. Theory and examples, Wadsworth & Brooks/Cole, Pacific Grove, CA, 1991. · Zbl 0709.60002 [16] Clement Dombry, Quelques applications de la theorie de grandes deviations, 1992. [17] Bruno Saussereau, Deviation probability bounds for fractional martingales and related remarks, Preprint submitted to Elsevier, 2012. · Zbl 1251.60036 [18] Ba Demba Bocar, On the fractional Brownian motion: Hansdorff dimension and Fourier expansion of fractional Brownian motion, Int. J. Adv. Appl. Math. and Mech. 5(2) (2017) 53-59. · Zbl 1425.60037 [19] Ba Demba Bocar, Moussa Thioune, Memoire de Master de l’universite de thies, 2015. [20] M. Klimek, M. Lupa, Reflection symmetric formulation of generalized fractional variational calculus, Fractional Calculus and Applied Analysis 16(1) (2013) 243-261 · Zbl 1312.26015 [21] R.P. Agarwa,l M. Benchohra, Samira Hamani, A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions, Acta Appl Math. 109(3) (2010) 973-1033. · Zbl 1198.26004 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.