Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. Numerical approximation schemes are invaluable tools for exploring its properties. In this paper, we introduce a class of stochastic age-dependent (vintage) capital system with Markovian switching, and investigate the convergence of numerical approximation. It is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions. A numerical example is provided to illustrate the theoretical results.

[1]  Natali Hritonenko,et al.  Turnpike and Optimal Trajectories in Integral Dynamic Models with Endogenous Delay , 2005 .

[2]  Natali Hritonenko,et al.  The optimal economic lifetime of vintage capital in the presence of operating costs, technological progress, and learning , 2008 .

[3]  Ronghua Li,et al.  Convergence and stability of numerical solutions to SDDEs with Markovian switching , 2006, Appl. Math. Comput..

[4]  S. Winter,et al.  An Evolutionary Theory of Economic Change.by Richard R. Nelson; Sidney G. Winter , 1987 .

[5]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[6]  D. Applebaum.  Lévy Processes and Stochastic Calculus: Preface , 2009 .

[7]  W. J. Anderson.  Continuous-Time Markov Chains , 1991 .

[8]  Gerald Silverberg,et al.  Long waves and 'evolutionary chaos' in a simple Schumpeterian model of embodied technical change , 1993 .

[9]  Zhang Qi-min,et al.  Existence, uniqueness and exponential stability for stochastic age-dependent population , 2004 .

[10]  M. Mariton,et al.  Jump Linear Systems in Automatic Control , 1992 .

[11]  P. Protter.  Stochastic integration and differential equations , 1990 .

[12]  Robert J. Elliott,et al.  PORTFOLIO OPTIMIZATION, HIDDEN MARKOV MODELS AND TECHNICAL ANALYSIS OF P&F CHARTS , 2002 .

[13]  P. Shi,et al.  Robust Kalman Filter Design for Markovian Jump Linear Systems with Norm-Bounded Unknown Nonlinearities , 2005 .

[14]  Chongzhao Han,et al.  Convergence of Numerical Solutions to Stochastic Age-Structured Population System , 2007, 2009 WRI Global Congress on Intelligent Systems.

[15]  Robert J. Elliott,et al.  American options with regime switching , 2002 .

[16]  P. Shi,et al.  Stochastic stability and robust control for sampled-data systems with Markovian jump parameters , 2006 .

[17]  Shaobo Zhou,et al.  Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching , 2009 .

[18]  X. Mao,et al.  Numerical solutions of stochastic differential delay equations under local Lipschitz condition , 2003 .

[19]  Xin Guo,et al.  Information and option pricings , 2001 .

[20]  Peter M. Kort,et al.  Capital accumulation under technological progress and learning: A vintage capital approach , 2006, Eur. J. Oper. Res..

[21]  Xuerong Mao,et al.  Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching , 2004, Math. Comput. Simul..

[22]  Anja Sturm,et al.  Stochastic Integration and Differential Equations. Second Edition. , 2005 .

[23]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[24]  Robert J. Elliott,et al.  Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching , 2007 .