Advanced search
Publication Cover
Stochastic Analysis and Applications Volume 39, 2021 - Issue 2
Submit an article Journal homepage
194
Views
5
CrossRef citations to date
0
Altmetric
Research Article

New stochastic operational matrix method for solving stochastic Itô–Volterra integral equations characterized by fractional Brownian motion

S. Saha RayDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela, IndiaCorrespondence[email protected]
&
S. SinghDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela, India
Pages 224-234 | Received 26 Apr 2019, Accepted 03 Jul 2020, Published online: 26 Jul 2020

References

  • Kolmogorov, A. N. (1940). Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. Acad. Sci. USSR (N.S.). 26:115–118.
  • Mandelbrot, B. B., Van Ness, J. W. (1968). Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10(4):422–437. DOI: 10.1137/1010093.
  • Taqqu, M. S. (2013). Benôıt Mandelbrot and fractional Brownian motion. Stat. Sci. 28(1):131–134. DOI: 10.1214/12-STS389.
  • Mirzaee, F., Hamzeh, A. (2017). Stochastic operational matrix method for solving stochastic differential equation by a fractional Brownian motion. Int. J. Appl. Comput. Math. 3(S1):411–425. DOI: 10.1007/s40819-017-0362-0.
  • Mohammadi, F. (2015). Haar wavelets approach for solving multidimensional stochastic Itô–Volterra integral equations. Appl. Math. E–Notes. 15:80–96.
  • Maleknejad, K., Khodabin, M., Rostami, M. (2012). Numerical solution of stochastic Volterra integral equations by a stochastic operational matrix based on block pulse functions. Math. Comput. Model. 55(3–4):791–800. DOI: 10.1016/j.mcm.2011.08.053.
  • Mohammadi, F., Adhami, P. (2016). Numerical study of stochastic Volterra-Fredholm integral equations by using second kind Chebyshev wavelets. Random Oper. Stoch. Equ. 24(2):129–141. DOI: 10.1515/rose-2016-0009.
  • Singh, S., Saha Ray, S. (2019). Stochastic operational matrix of Chebyshev wavelets for solving multi-dimensional stochastic Itô-Volterraintegral equations. Int. J. Wavelets Multi. Inf. Process. 17(3):1950007. DOI: 10.1142/S0219691319500073.
  • Saha Ray, S. (2020). Nonlinear Differential Equations in Physics. Singapore: Springer Nature.
  • Saha Ray, S., Singh, S. (2018). Numerical solutions of stochastic Volterra–Fredholm integral equations by hybrid Legendre block-pulse functions. Int. J. Nonlinear Sci. Numer. Simul. 19(3–4):289–297. DOI: 10.1515/ijnsns-2017-0038.
  • Saha Ray, S., Gupta, A. K. (2016). Numerical solution of fractional partial differential equation of parabolic type with Dirichlet boundary conditions using two-dimensional Legendre wavelets method. J. Comput. Nonlinear Dyn.. 11(1):9. DOI: 10.1115/1.4028984.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.