Estimates for the difference between approximate and exact solutions to stochastic differential equations in the G-framework

References

• Zamana G, Kang YH, Jung IH. Stability analysis and optimal vaccination of an SIR epidemic model. BioSystems. 2008;93:240–249. doi: 10.1016/j.biosystems.2008.05.004
   Web of Science ®Google Scholar
• Zaman G, Kang YH, Cho G, et al. Optimal strategy of vaccination & treatment in an SIR epidemic model. Math Comput Simul. 2017;136:63–77. doi: 10.1016/j.matcom.2016.11.010
   Web of Science ®Google Scholar
• Khan L, Ali F, Shah NA. Interaction of magnetic field with heat and mass transfer in free convection flow of a Walters'-B fluid. Eur Phys J Plus. 2016;131(77):1–15.
   Google Scholar
• Peng S. Multi-dimentional G-Brownian motion and related stochastic calculus under G-expectation. Stoch Process Appl. 2008;12:2223–2253. doi: 10.1016/j.spa.2007.10.015
   Google Scholar
• Peng S. G-expectation, G-Brownian motion and related stochastic calculus of Ito's type. In: Benth et al., editors. The Abel symposium 2005, Abel symposia 2. Berlin: Springer-verlag; 2006. p. 541–567.
   Google Scholar
• Gao F. Pathwise properties and homeomorphic flows for stochastic differential equations driven by G-Brownian motion. Stoch Process Appl. 2009;10:3356–3382. doi: 10.1016/j.spa.2009.05.010
   Google Scholar
• Faizullah F. A note on the Caratheodory approximation scheme for stochastic differential equations under G-Brownian motion. Z Naturforschung A. 2012;67a:699–704.
   Google Scholar
• Bai X, Lin Y. On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with Integral-Lipschitz coefficients. Acta Math Appl Sin. 2014;30(3):589–610. doi: 10.1007/s10255-014-0405-9
   Web of Science ®Google Scholar
• Faizullah F. Existence of solutions for stochastic differential equations under G-Brownian motion with discontinuous coefficients. Z Naturforschung A. 2012;67a:692–698.
   Google Scholar
• Denis L, Hu M, Peng S. Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal. 2010;34:139–161. doi: 10.1007/s11118-010-9185-x
   Web of Science ®Google Scholar
• Ullah R, Faizullah F. On existence and approximate solutions for stochastic differential equations in the framework of G-Brownian motion. Eur Phys J Plus. 2017;132:435–443. doi: 10.1140/epjp/i2017-11700-9
   Web of Science ®Google Scholar
• Gao F, Jiang H. Approximation Theorem for Stochastic Differential Equations Driven by G-Brownian Motion. Prog Probab. 2011;65:73–81.
   Google Scholar
• Gu Y, Ren Y, Sakthivel R. Square-mean pseudo almost automorphic mild solutions for stochastic evolution equations driven by G-Brownian motion. Stoch Anal Appl. 2016;34(3):528–545. doi: 10.1080/07362994.2016.1155159
   Web of Science ®Google Scholar
• Li X, Peng S. Stopping times and related Ito's calculus with G-Brownian motion. Stoch Process Appl. 2011;121:1492–1508. doi: 10.1016/j.spa.2011.03.009
   Web of Science ®Google Scholar
• Luo P, Wang F. Stochastic differential equations driven by G-Brownian motion and ordinary differential equations. Stoch Process Appl. 2014;124:3869–3885. doi: 10.1016/j.spa.2014.07.004
   Web of Science ®Google Scholar
• Song Y. Properties of hitting times for G-martingale and their applications. Stoch Process Appl. 2011;121(8):1770–1784. doi: 10.1016/j.spa.2011.04.007
   Web of Science ®Google Scholar
• Xua J, Zhang B. Martingale characterization of G-Brownian motion. Stoch Process Appl. 2009;119:232–248. doi: 10.1016/j.spa.2008.02.001
   Web of Science ®Google Scholar
• Mao X. Stochastic differentail equations and their applications. Chichester, England: Horwood Publishing; 1997.
   Google Scholar
• Ren Y, Bi Q, Sakthivel R. Stochastic functional differential equations with infinite delay driven by G-Brownian motion. Math Methods Appl Sci. 2013;36(13):1746–1759. doi: 10.1002/mma.2720
   Web of Science ®Google Scholar
• Faizullah F. Existence and uniqueness of solutions to SFDEs driven by G-Brownian motion with non-Lipschitz conditions. J Comput Anal Appl. 2017;2(23):344–354.
   Google Scholar
• Faizullah F. Stochastic functional differential equations driven by G-Browniain motion with monotone nonlinearity. 2018. Available from: https://arxiv.org/abs/1806.07824.
   Google Scholar
• Faizullah F. Existence and asymptotic properties for the solutions to nonlinear SFDEs driven by G-Brownian motion with infinite delay. 2018. Available from: https://arxiv.org/abs/1805.10658.
   Google Scholar
• Faizullah F, Rehman M-U, Shehzad M, et al. On existence and comparison results for solutions to stochastic functional differential equations in the G-framework. J Comput Anal Appl. 2017;4(23):693–702.
   Google Scholar
• Faizullah F. On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework. SpringerPlus. 2016;5(872):1–11.
   PubMedGoogle Scholar
• Faizullah F. A note on pth moment estimates for stochastic functional differential equations in the framework of G-Brownian motion,Iranian Journal of Science and Technology. Trans. A. 2016;3(40):1–8.
   Google Scholar
• Faizullah F. Existence results and moment estimates for NSFDEs driven by G-Brownian motion. J Comput Theor Nanosci. 2016;7(13):1–8.
   Google Scholar