Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30184
Exponential Stability of Numerical Solutions to Stochastic Age-Dependent Population Equations with Poisson Jumps

Authors: Mao Wei

Abstract:

The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-dependent population equations with Poisson random measures. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.

Keywords: Stochastic age-dependent population equations, poisson random measures, numerical solutions, exponential stability.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329208

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1018

References:


[1] J.H.Pollard, On the use of the direct matrix product in analyzing certain stochastic population model, Biometrika. 53(1966), 397-415.
[2] Q.M.Zhang, W.A.Liu, Z.K.Nie, Existence, uniqueness and exponential stability for stochastic age-dependent population, Appl. Math. Comput. 154(2004), 183-201.
[3] Li Ronghua, Meng Hongbing, Chang Qin, Convergence of numerical solutions to stochastic age-dependent population equations. J. Comput. Appl. Math. 193(2006), 109-120.
[4] W.K. Pang, Li Ronghua, Liu Ming, Exponential stability of numerical solutions to stochastic age-dependent population equations. Appl. Math. Comput. 183(2006), 152-159.
[5] Ronghua Li, W.K. Pang, Qinghe Wang. Numerical analysis for stochastic age-dependent population equations with Poisson jumps. J. Math. Anal. Appl, 327(2007), 1214-1224.
[6] Wang L, Wang X, Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps. Appl. Math. Model. 34(2010), 2034-2043.
[7] D. J. Higham, X. Mao, C.Yuan, Almost Sure and Moment Exponential Stability in the Numerical Simulation of Stochastic Differential Equations. SIAM. J. Numer. Anal, vol. 45, 2007, pp. 592-609.
[8] Xuerong Mao, Exponential stability of equidistant EulerCMaruyama approximations of stochastic differential delay equations J. Comput. Appl. Math. 200, 2007, 297-316
[9] D.J.Higham, X.Mao, and A.M.Stuart, Exponential Mean-Square Stability of Numerical Solutions to Stochastic Differential Equations, LMS J. Comput. Math, 6(2003), 297-313.
[10] N.Ikeda and S.Watanable, Stochastic Differential Equations and diffusion processes, North-Holland/ Kodansha Amsterdam. Oxford. New York. 1989.