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Mean-square dissipative methods for stochastic age-dependent capital system with fractional Brownian motion and jumps

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  • Li, Qiang
  • Kang, Ting
  • Zhang, Qimin

Abstract

In this paper, we analyze mean-square dissipativity of numerical methods applied to a class of stochastic age-dependent (vintage) capital system with fractional Brownian motion (fBm) and Poisson jumps. Some sufficient conditions are obtained for ensuring the underlying systems are mean-square dissipative. It is shown that the mean-square dissipativity is preserved by the compensated split-step backward Euler method and compensated backward Euler method without any restriction on stepsize, while the split-step backward Euler method and backward Euler method could reproduce mean-square dissipativity under a stepsize constraint. Those results indicate that compensated numerical methods achieve superiority over non-compensated numerical methods in terms of mean-square dissipativity. A numerical example is provided to illustrate the theoretical results.

Suggested Citation

  • Li, Qiang & Kang, Ting & Zhang, Qimin, 2018. "Mean-square dissipative methods for stochastic age-dependent capital system with fractional Brownian motion and jumps," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 81-92.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:81-92
    DOI: 10.1016/j.amc.2018.07.018
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    References listed on IDEAS

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    1. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Capital accumulation under technological progress and learning: A vintage capital approach," European Journal of Operational Research, Elsevier, vol. 172(1), pages 293-310, July.
    2. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    3. Feichtinger, Gustav & Hartl, Richard F. & Kort, Peter M. & Veliov, Vladimir M., 2006. "Anticipation effects of technological progress on capital accumulation: a vintage capital approach," Journal of Economic Theory, Elsevier, vol. 126(1), pages 143-164, January.
    4. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    5. Goetz, Renan-Ulrich & Hritonenko, Natali & Yatsenko, Yuri, 2008. "The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 3032-3053, September.
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    Cited by:

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    2. He, Lingyun & Banihashemi, Seddigheh & Jafari, Hossein & Babaei, Afshin, 2021. "Numerical treatment of a fractional order system of nonlinear stochastic delay differential equations using a computational scheme," Chaos, Solitons & Fractals, Elsevier, vol. 149(C).

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