AN APPROACH TO PATHWISE STOCHASTIC INTEGRATION IN FRACTIONAL BESOV-TYPE SPACES BY KRYLOV INEQUALITY
Keywords:
Besov space, Wiener integral, fractional Brownian motion, Ito process, stochastic differential equation.DOI:
https://doi.org/10.17654/2277141723005Abstract
In this paper, we consider the approach to pathwise stochastic integration in fractional Besov-types spaces introduced by Nualart in the case 
In the case 
we used an approach based on the weak solutions and the inequality of Krylov.
Received: October 6, 2022;
Accepted: November 15, 2022;
References
M. Alhagyan, M. Misiran and O. Zurni, New proof of the theorem of existence and uniqueness of geometric fractional Brownian motion equation, Global Journal of Pure and Applied Mathematics 12(6) (2016), 4759-4769.
E. Alos, J. L. Leon and D. Nualart, Stochastic Stratonovich calculus fBm for fractional Brownian motion with Hurst parameter less than Taiwanese J. Math. 5 (2001), 609-632.
Demb Bocar Ba and M. Thioune, Consistency of the drift parameters estimates in the fractional Brownian diffusion model and estimation of the Hurst parameter by maximum likelihood method, Journal of Computer Science and Applied Mathematics 4(1) (2020), 1-14. Doi: 10.37418/jcsam.4.1.1.
P. J. Bickel and K. A. Doksum, Mathematical Statistics, Prentice Hall, Inc., 1977.
Christos H. Skiadas, Exact solutions of stochastic differential equations: Gompertz, Generalized Logistic and Revised Exponential, Methodol. Comput. Appl. Probab. 12 (2010), 261-270.
Diop Bou, Ba Demba Bocar and Thioune Moussa Thioune, Method of construction of the stochastic integral with respect to fractional Brownian motion, American Journal of Applied Mathematics 9(5) (2021), 156-164. Doi: 10.11648/j.ajam.20210905.11
D. Nualart, Stochastic calculus with respect to fractional Brownian motion and applications, Contemporary Mathematics 336 (2003), 3-39.
F. Russo and P. Vallois, Elements of stochastic calculus via regularization, Séminaire de Probabilitiés XL, 2005, pp. 147-185.
F. Russo and P. Vallois, The generalized covariation process and Itô formula, Stochastic Processes and their Application 59 (1995), 81-104.
M. Gradinaru and I. Nourdin, Stochastic volatility: approximation and goodness-of-fit test, Preprint 2003-53.
M. Gradinaru and I. Nourdin, Approximation at first and second order of m-order integrals of the fractional Brownian motion and of certain semimartingales, Electron J. Probab. 8(18) (2003), 1-26.
M. Gradinaru, I. Nourdin, F. Russo and P. Vallois, m-order integrals and generalized Ito’s formula; the case of a fractional Brownien notion with any Hurst index, Annales de l’I.H.P. Probabilités et statistiques 41 (2005), 781-806.
H. Doss, Links between stochastic and ordinary differential equations, Ann. Inst. Henri Poincar 13 (1977), 99-125.
L. Coutin and Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motion, Probab. Theory Related 122(1) (2002), 108-140.
M. Stefano Lucas, Simulation and Inference for Statistics Differential Equations with R Examples, Springer Series in Statistics, 2016.
Thioune Moussa, Ba Demba Bocar and Diop Bou, Study of models without jumps with respect to fractional Brownian motion, Journal of Computer Science and Applied Mathematics 4(1) (2002), 15-30. Doi: 10.37418/jcsam.4.1.2
W. Dai and C. C. Heyde, Ito formula with respect to fractional Brownian motion and its applications, International Journal of Stochastic Analysis 9(4) (1996), 439-448.
L. C. Young, An inequality of the Holder type, connected with Stieltjes integration, Acta Math. 67 (1936), 251-282.
A. Ayache, D. Wu and Y. Xiao, Asymptotic properties and Hausdorff dimensions of fractional Brownian sheets, J. Fourier Anal. Appl. 11 (2005), 407-439.
Ba Demba Bocar, On the fractional Brownian motion: Hausdorff dimension and Fourier expansion of fractional Brownian motion, International Journal of Advances in Applied Mathematical and Mechanics 5 (2017), 53-59.
F. Baudoin and D. Nualart, Equivalence of Volterra processes, Stochastic Processes and their Applications 107(2) (2003), 327-350.
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
A. Benassi, P. Bertrand, S. Cohen and J. Istas, Identification of the Hurst index of a step fractional Brownian motion, Statistical Inference for Stochastic Processes 3 (2000), 101-111.
C. Houdre and J. Villa, An example of infinite dimensional quasi-Helix, Contemporary Mathematics (American Mathematical Society) 336 (2003), 195 201.
M. Maejima and C. Tudor, Limits of bifractional Brownian noises, Commun. Stoch. Anal. 2 (2008), 369-383.
F. Russo and C. Tudor, On the bifractional Brownian motion, Stochastic Processes and their Applications 116 (2006), 830-856.
Shiqui Song, Quelques conditions suffisantes pour qu’une semimartingale soit une quasi-martingale, Stochastics 16 (1986), 97-109.
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