Geodesic
Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
Zheng, Lai-Yun 1 ; Zhang, Qi-Min 2
1 School of Mechanical Engineering, Ningxia University, Yinchuan 750021, China
2 School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China
Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 9, p. 4597-4610.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we consider a class of stochastic age-dependent capital system with fractional Brownian motion, and investigate the convergence of numerical approximate solution. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under given conditions. A numerical example is provided to illustrate the theoretical results.
DOI : 10.22436/jnsa.010.09.04
Classification : 65C35, 60G22, 65M12
Keywords: Stochastic age-dependent capital system, numerical solution, Euler approximation, fractional Brownian motion.

Zheng, Lai-Yun  1 ; Zhang, Qi-Min  2

1 School of Mechanical Engineering, Ningxia University, Yinchuan 750021, China
2 School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China 
@article{JNSA_2017_10_9_a3,
     author = {Zheng, Lai-Yun  and Zhang, Qi-Min },
     title = {Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional {Brownian} motion},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {4597-4610},
     publisher = {mathdoc},
     volume = {10},
     number = {9},
     year = {2017},
     doi = {10.22436/jnsa.010.09.04},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.09.04/}
}
TY  - JOUR
AU  - Zheng, Lai-Yun 
AU  - Zhang, Qi-Min 
TI  - Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
JO  - Journal of nonlinear sciences and its applications
PY  - 2017
SP  - 4597
EP  - 4610
VL  - 10
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.09.04/
DO  - 10.22436/jnsa.010.09.04
LA  - en
ID  - JNSA_2017_10_9_a3
ER  - 
%0 Journal Article
%A Zheng, Lai-Yun 
%A Zhang, Qi-Min 
%T Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
%J Journal of nonlinear sciences and its applications
%D 2017
%P 4597-4610
%V 10
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.09.04/
%R 10.22436/jnsa.010.09.04
%G en
%F JNSA_2017_10_9_a3
Zheng, Lai-Yun ; Zhang, Qi-Min . Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion. Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 9, p. 4597-4610. doi : 10.22436/jnsa.010.09.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.09.04/

[1] J. F. Coeurjolly Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study, J. Stat. Softw., Volume 5 (2000), pp. 1-53

[2] Du, Q.-H.; C.-L. Wang Convergence analysis of semi-implicit Euler methods for solving stochastic age-dependent capital system with variable delays and random jump magnitudes , Math. Probl. Eng., Volume 2014 (2014), pp. 1-12

[3] Duncan, T. E.; Maslowski, B.; Pasik-Duncan, B. Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise, Stochastic Process. Appl., Volume 115 (2005), pp. 1357-1383 | Zbl | DOI

[4] Feichtinger, G.; Hartl, R. F.; Kort, P. M.; V. M. Veliov Anticipation effects of technological progress on capital accumulation: a vintage capital approach, J. Econom. Theory, Volume 126 (2006), pp. 143-164 | DOI | Zbl

[5] Feichtinger, G.; Hartl, R. F.; Kort, P. M.; V. M. Veliov Vladimir, Capital accumulation under technological progress and learning: a vintage capital approach , Eur. J. Oper. Res., Volume 172 (2006), pp. 293-310 | DOI

[6] Goetz, R. U.; Hritonenko, N.; Yatsenko, Y. The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning , J. Econom. Dynam. Control, Volume 32 (2008), pp. 3032-3053 | Zbl | DOI

[7] Gu, H.; Liang, J.-R.; Zhang, Y.-X. Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Phys. A, Volume 391 (2012), pp. 3971-3977 | DOI

[8] K. Jańczak-Borkowska Generalized BSDEs driven by fractional Brownian motion, Statist. Probab. Lett., Volume 83 (2013), pp. 805-811 | Zbl | DOI

[9] Jiang, Y.-M.; Wang, X.-C.; Wang, Y.-J. On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal. Appl., Volume 396 (2012), pp. 656-669 | DOI | Zbl

[10] Kloeden, P. E.; Platen, E. Numerical solution of stochastic differential equations, Applications of Mathematics (New York), Springer-Verlag, Berlin, 1992 | DOI

[11] Ma, W.-J.; Zhang, Q.-M.; Han, C.-Z. Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul., Volume 17 (2012), pp. 1884-1893 | DOI | Zbl

[12] A. Rathinasamy Split-step \(\theta\)-methods for stochastic age-dependent population equations with Markovian switching, Nonlinear Anal. Real World Appl., Volume 13 (2012), pp. 1334-1345 | Zbl | DOI

[13] Ronghua, L.; P.Wan-kai; L. Ping-kei Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching, Appl. Math. Comput., Volume 216 (2010), pp. 744-752 | Zbl | DOI

[14] Rostek, S.; R. Schöbel A note on the use of fractional Brownian motion for financial modeling, Econ. Model., Volume 30 (2013), pp. 30-35 | DOI

[15] Wang, J.; Liang, J.-R.; Lv, L.-J.; Qiu, W.-Y.; Ren, F.-Y. Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime, Phys. A, Volume 391 (2012), pp. 750-759 | DOI

[16] Xiao, W.-L.; Zhang, W.-G.; Zhang, X.-L.; Y.-L. Wang Pricing currency options in a fractional Brownian motion with jumps, Econ. Model., Volume 27 (2010), pp. 935-942 | DOI

[17] Xiao, W.-L.; Zhang, W.-G.; Zhang, X.-L.; X.-L. Zhang Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm, Phys. A, Volume 391 (2012), pp. 6418-6431 | DOI

[18] Q.-M. Zhang Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion, J. Comput. Appl. Math., Volume 220 (2008), pp. 22-33 | DOI | Zbl

[19] Zhang, Q.-M.; C.-Z. Han Numerical analysis for stochastic age-dependent population equations, Appl. Math. Comput., Volume 169 (2005), pp. 278-294 | DOI

[20] Zhang, Q.-M.; Liu, Y.-T.; X.-N. Li Strong convergence of split-step backward Euler method for stochastic age-dependent capital system with Markovian switching, Appl. Math. Comput., Volume 235 (2014), pp. 439-453 | DOI | Zbl

[21] Zhang, Q.-M.; Pang, W.-K.; P.-K. Leung Exponential stability of numerical solutions for a class of stochastic age-dependent capital system with Poisson jumps , J. Comput. Appl. Math., Volume 235 (2011), pp. 3369-3377 | DOI | Zbl

[22] Zhang, Q.-M.; Rathinasamy, A. Convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes, Appl. Math. Comput., Volume 219 (2013), pp. 7297-7305 | Zbl | DOI

Cité par Sources :