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Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations

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  • Xiao, Guanli
  • Wang, JinRong
  • O’Regan, Donal

Abstract

In this paper, we study conformable stochastic differential equations. Firstly, the Itô formula is established and used to discuss the explicit expression of solutions of linear differential equations. Secondly, the existence and uniqueness of solutions of nonlinear conformable stochastic differential equations are proved by the Picard iteration method, and the continuous dependence of solutions on initial values is proved by the Gronwall inequality, the exponential estimation of solutions is also given. Finally, some examples are given to illustrate the theoretically results and we compare the simulation results for the conformable stock model with different ρ.

Suggested Citation

  • Xiao, Guanli & Wang, JinRong & O’Regan, Donal, 2020. "Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920306652
    DOI: 10.1016/j.chaos.2020.110269
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    References listed on IDEAS

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    1. Zhao, Dazhi & Pan, Xueqin & Luo, Maokang, 2018. "A new framework for multivariate general conformable fractional calculus and potential applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 271-280.
    2. Hu, Mingshang & Ji, Shaolin & Peng, Shige & Song, Yongsheng, 2014. "Backward stochastic differential equations driven by G-Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 759-784.
    3. Song, Yongsheng, 2019. "Properties of G-martingales with finite variation and the application to G-Sobolev spaces," Stochastic Processes and their Applications, Elsevier, vol. 129(6), pages 2066-2085.
    4. Peng, Shige, 2008. "Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation," Stochastic Processes and their Applications, Elsevier, vol. 118(12), pages 2223-2253, December.
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    2. Kaviya, R. & Priyanka, M. & Muthukumar, P., 2022. "Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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