Abstract
In this paper, stochastic age-structure population system with jump are studied. It is proved that the semi-implicit Euler approximation solutions converge to the analytic solution for the stochastic age-structured population system with Poisson jump. The analysis use Itô′s formula, Burkholder-Davis-Gundy’s inequality, Gronwall’s lemma and some inequalities for our purposes.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Hernandez, G.E.: Age-density dependent population dispersal in R N. Mathematical Biosciences J. 149, 37–56 (1998)
Hernandez, G.E.: Existence of solutions in a population dynamic problem. J. Appl. Math. 509, 43–48 (1986)
Hernandez, G.E.: Localization of age-dependent ant-crowding populations. J. Q. Appl. Math. 53, 35 (1995)
Zhang, Q., Han, C.Z.: existence and uniqueness for a stochastic age-structured population system with diffusion. J. Science Direct 32, 2197–2206 (2008)
Zhang, Q., Liu, W., Nie, Z.: Existence, uniqueness and exponential stability of stochastic age-dependent population. J. Appl. Math. Comput. 154, 183–201 (2004)
Zhang, Q., Han, C.Z.: Convergence of numerical solutions to stochastic age-structured population system with diffusion. J. Applied Mathematics and Computation 07, 156 (2006)
Zhang, Q.: Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion. Journal of Computational and Applied Mathematics 220, 22–33 (2008)
Zhang, Q., Han, C.Z.: Numerical analysis for stochastic age-dependent population equations. J. Appl. Math. Comput. 176, 210–223 (2005)
Gardon, A.: The Order of approximations for solutions of Ito-type stochastic differential equations with jumps. J. Stochastic Analysis and Applications 38, 753–769 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ma, D., Zhang, Q. (2011). Convergence of the Stochastic Age-Structured Population System with Diffusion. In: Lin, S., Huang, X. (eds) Advances in Computer Science, Environment, Ecoinformatics, and Education. CSEE 2011. Communications in Computer and Information Science, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23321-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-23321-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-23320-3
Online ISBN: 978-3-642-23321-0
eBook Packages: Computer ScienceComputer Science (R0)