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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 4
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Research Article

BSDEs driven by fractional Brownian motion with time-delayed generators

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Pages 724-733 | Received 11 Nov 2022, Accepted 14 Apr 2023, Published online: 08 May 2023

References

  • Pardoux E, Peng S. Adapted solution of a backward stochastic differential equation. Systems & Control Letters. 1990;14(1):55–61.
  • Pardoux E, Peng S. Backward stochastic differential equations and quasilinear parabolic PDEs. In: Rozosvskii BL, Sowers RS, editors. Stochastic partial differential equations and their applications. Berlin, Heidelberg, New York: Springer; p. 200–217. (Lecture Notes in Control and Information Sciences; vol. 176).
  • Aidara S. Anticipated backward doubly stochastic differential equations with stochastic Lipschitzian coefficients. J Numer Math Stoch. 2018;10(1):94–110.
  • Wang Y, Huang Z. Backward stochastic differential equations with non Lipschitz coefficients. Stat Probab Lett. 2009;79:1438–1443.
  • Aidara S, Sow AB. Generalized fractional BSDE with non Lipschitz coefficients. Afr Mat. 2016;27(3–4):443–455.
  • Mao X. Adapted solution of backward stochastic differential equations with non-Lipschitz coefficients. Stoch Process Their Appl. 1997;58:281–292.
  • Aidara S, Sagna Y. Backward stochastic differential equations driven by two mutually independent fractional Brownian motions with stochastic Lipschitz condition. Appl Math Nonlinear Sci. 2019;4(1):151–162.
  • Delong L, Imkeller P. Backward stochastic differential equations with time delayed generators – results and conterexamples. Ann Appl Probab. 2010;20(4):1512–1536.
  • Bender C. Explicit solutions of a class of linear fractional BSDEs. Syst Control Lett. 2005;54:671–680.
  • Hu Y, Peng S. Backward stochastic differential equation driven by fractional Brownian motion. SIAM J Control Optim. 2009;48(3):1675–1700.
  • Maticiuc L, Nie T. Fractional backward stochastic differential equations and fractional backward variational inequalities, 2012. arXiv preprint Arxiv: 1102.3014v3[mathPR].
  • Hu Y. Integral transformation and anticipative calculus for fractional Brownian motion. Mem Amer Math Soc. Vol. 175, 2005
  • Elliot JR. Ito formulas for fractional Brownian motion. Haskayne School of Business, University of Calgary.
  • Guo Y, Chen M, Shu XB, et al. The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm. Stoch Anal Appl. 2021, 39(4), 643-666.
  • Ma X, Shu X-B. Existence of almost periodic solutions for fractional impulsive neutral stochastic differential equations with infinite delay. Stoch Dyn. 2020;20(1):2050003.(31 pages).
  • Imkeller P. Malliavin's calculus and applications in stochastic control and finance. Warsaw, March, April 2008, version of 5. 2008 Apr.
  • Hu Y, Nualart D, Song J. fractional martingales and characterization of the fractional brownian motion. Ann Probab. 2009;37(6):2404–2430.

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