publication . Article . 2018

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Xiao-Li Ding; Juan J. Nieto;
Open Access
  • Published: 16 Jan 2018 Journal: Entropy, volume 20, page 63 (eissn: 1099-4300, Copyright policy)
  • Publisher: MDPI AG
  • Country: Colombia
Abstract
In this paper, we investigate analytical solutions of multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. We firstly decompose homogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions into independent differential subequations, and give their analytical solutions. Then, we use the variation of constant parameters to obtain the solutions of nonhomogeneous multi-time scale fractional stochastic differential equations driven by fractional Brownian motions. Finally, we give three examples to demonstrate the applicability of our obtained results The work of the Xia...
Subjects
free text keywords: Multi-time scale fractional stochastic differential equations, Fractional stochastic partial differential equation, Analytical solution, General Physics and Astronomy, Applied mathematics, Mathematics, Homogeneous, Brownian motion, Mathematical optimization, Fractional Brownian motion, Stochastic differential equation, Science, Q, Astrophysics, QB460-466, Physics, QC1-999
Related Organizations
41 references, page 1 of 3

Water Resour. Res. 2000, 36, 1403-1412.

Hilfer, R. Applications of Fractional Calculus in Physics; World Scientific: Singapore, 2000.

Vázquez, J.L. The mathematical theories of diffusion: Nonlinear and fractional diffusion. In Lecture Notes in Mathematics; Morel, J.-M., Cachan, ENS, Teissier, B., Paris 7, U., Eds; Springer: Berlin/Heidelberg, Germany, 2017, pp. 205-278.

4. Hall, M.G.; Barrick, T.R. From diffusion-weighted MRI to anomalous diffusion imaging. Magn. Reson. Med. 2008, 59, 447-455.

5. Cesbron, L.; Mellet, A.; Trivisa, K. Anomalous transport of particles in plasma physics. Appl. Math. Lett. 2012, 25, 2344-2348. [OpenAIRE]

6. Metzler, R.; Klafter, J. The random walk's guide to anomalous diffusion: A fractional dynamics approach. Phys. Rep. 2000, 339, 1-77.

7. Postnikov, E.B.; Sokolov, I.M. Model of lateral diffusion in ultrathin layered films. Phys. A 2012, 391, 5095-5101.

8. Wang, Y.; Zheng, S.; Zhang, W.; Wang, J. Complex and Entropy of Fluctuations of Agent-Based Interacting Financial Dynamics with Random Jump. Entropy 2017, 19, 512, doi:10.3390/e19100512.

9. San-Millan, A.; Feliu-Talegon, D.; Feliu-Batlle, V.; Rivas-Perez, R. On the Modelling and Control of a Laboratory Prototype of a Hydraulic Canal Based on a TITO Fractional-Order Model. Entropy 2017, 19, 401, doi:10.3390/e19080401.

10. Alsaedi, A.; Nieto, J.J.; Venktesh, V. Fractional electrical circuits. Adv. Mech. Eng. 2015, 7, 1-7.

11. Ladde, G.S.; Wu, L. Development of nonlinear stochastic models by using stock price data and basic statistics. Neutral Parallel Sci. Comput. 2010, 18, 269-282.

12. Tien, D.N. Fractional stochastic differential equations with applications to finance. J. Math. Anal. Appl. 2013, 397, 334-348.

13. Farhadi, A.; Erjaee, G.H.; Salehi, M. Derivation of a new Merton's optimal problem presented by fractional stochastic stock price and its applications. Comput. Math. Appl. 2017, 73, 2066-2075. [OpenAIRE]

14. Arnold, L. Stochastic Differential Equations: Theory and Applications; Wiley: New York, NY, USA, 1974.

15. Mandelbrot, B.; Van Ness, J. Fractional Brownian motions, fractional noises and applications. SIAM Rev. 1968, 10, 422-437. [OpenAIRE]

41 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . 2018

Analytical Solutions for Multi-Time Scale Fractional Stochastic Differential Equations Driven by Fractional Brownian Motion and Their Applications

Xiao-Li Ding; Juan J. Nieto;