Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion
-
2509
Downloads
-
3515
Views
Authors
Lai-Yun Zheng
- School of Mechanical Engineering, Ningxia University, Yinchuan 750021, China.
Qi-Min Zhang
- School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China.
Abstract
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.
Share and Cite
ISRP Style
Lai-Yun Zheng, Qi-Min Zhang, Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 9, 4597--4610
AMA Style
Zheng Lai-Yun, Zhang Qi-Min, Convergence of numerical solutions for a class of stochastic age-dependent capital system with fractional Brownian motion. J. Nonlinear Sci. Appl. (2017); 10(9):4597--4610
Chicago/Turabian Style
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 Applications, 10, no. 9 (2017): 4597--4610
Keywords
- Stochastic age-dependent capital system
- numerical solution
- Euler approximation
- fractional Brownian motion.
MSC
References
-
[1]
J. F. Coeurjolly , Simulation and identification of the fractional Brownian motion: a bibliographical and comparative study, J. Stat. Softw., 5 (2000), 1–53.
-
[2]
Q.-H. Du, 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., 2014 (2014), 12 pages.
-
[3]
T. E. Duncan, B. Maslowski, B. Pasik-Duncan, Stochastic equations in Hilbert space with a multiplicative fractional Gaussian noise, Stochastic Process. Appl., 115 (2005), 1357–1383.
-
[4]
G. Feichtinger, R. F. Hartl, P. M. Kort, V. M. Veliov , Anticipation effects of technological progress on capital accumulation: a vintage capital approach, J. Econom. Theory, 126 (2006), 143–164.
-
[5]
G. Feichtinger, R. F. Hartl, P. M. Kort, V. M. Veliov , Vladimir, Capital accumulation under technological progress and learning: a vintage capital approach , Eur. J. Oper. Res., 172 (2006), 293–310.
-
[6]
R. U. Goetz, N. Hritonenko, Y. Yatsenko, The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning , J. Econom. Dynam. Control, 32 (2008), 3032–3053.
-
[7]
H. Gu, J.-R. Liang, Y.-X. Zhang, Time-changed geometric fractional Brownian motion and option pricing with transaction costs, Phys. A, 391 (2012), 3971–3977.
-
[8]
K. Jańczak-Borkowska , Generalized BSDEs driven by fractional Brownian motion, Statist. Probab. Lett., 83 (2013), 805–811.
-
[9]
Y.-M. Jiang, X.-C. Wang, Y.-J. Wang, On a stochastic heat equation with first order fractional noises and applications to finance, J. Math. Anal. Appl., 396 (2012), 656–669.
-
[10]
P. E. Kloeden, E. Platen, Numerical solution of stochastic differential equations, Applications of Mathematics (New York), Springer-Verlag, Berlin (1992)
-
[11]
W.-J. Ma, Q.-M. Zhang, C.-Z. Han, Numerical analysis for stochastic age-dependent population equations with fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 1884–1893.
-
[12]
A. Rathinasamy , Split-step \(\theta\)-methods for stochastic age-dependent population equations with Markovian switching, Nonlinear Anal. Real World Appl., 13 (2012), 1334–1345.
-
[13]
L. Ronghua, P.Wan-kai, L. Ping-kei , Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching, Appl. Math. Comput., 216 (2010), 744–752.
-
[14]
S. Rostek, R. Schöbel , A note on the use of fractional Brownian motion for financial modeling, Econ. Model., 30 (2013), 30–35.
-
[15]
J. Wang, J.-R. Liang, L.-J. Lv, W.-Y. Qiu, F.-Y. Ren, Continuous time Black-Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime, Phys. A, 391 (2012), 750–759.
-
[16]
W.-L. Xiao, W.-G. Zhang, X.-L. Zhang, Y.-L. Wang , Pricing currency options in a fractional Brownian motion with jumps, Econ. Model., 27 (2010), 935–942.
-
[17]
W.-L. Xiao, W.-G. Zhang, X.-L. Zhang, X.-L. Zhang , Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm, Phys. A, 391 (2012), 6418–6431.
-
[18]
Q.-M. Zhang , Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion, J. Comput. Appl. Math., 220 (2008), 22–33.
-
[19]
Q.-M. Zhang, C.-Z. Han , Numerical analysis for stochastic age-dependent population equations, Appl. Math. Comput., 169 (2005), 278–294.
-
[20]
Q.-M. Zhang, Y.-T. Liu, X.-N. Li , Strong convergence of split-step backward Euler method for stochastic age-dependent capital system with Markovian switching, Appl. Math. Comput., 235 (2014), 439–453.
-
[21]
Q.-M. Zhang, W.-K. Pang, P.-K. Leung , Exponential stability of numerical solutions for a class of stochastic age-dependent capital system with Poisson jumps , J. Comput. Appl. Math., 235 (2011), 3369–3377.
-
[22]
Q.-M. Zhang, A. Rathinasamy, Convergence of numerical solutions for a class of stochastic age-dependent capital system with random jump magnitudes, Appl. Math. Comput., 219 (2013), 7297–7305.
