×

Numerical analysis for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching. (English) Zbl 1221.65019

Summary: We shall examine the convergence of semi-implicit Euler approximation for stochastic age-dependent population equations with Poisson jump and phase semi-Markovian switching. Here, the main ideas from the papers [R. Li, P.-K. Leung and W.-K. Pang, J. Comput. Appl. Math. 233, No. 4, 1046–1055 (2009; Zbl 1180.65008)] and [L. Wang and X. Wang, Appl. Math. Modelling 34, No. 8, 2034–2043 (2010; Zbl 1193.60089)] are successfully developed to the more general cases. Finally, a numerical example is provided to illustrate the theoretical result of convergence.

MSC:

65C30 Numerical solutions to stochastic differential and integral equations
60J75 Jump processes (MSC2010)
60K15 Markov renewal processes, semi-Markov processes
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Brewer, J.W., The age-dependent eigenfunctions of certain Kolmogorov equations of engineering, economics, and biology, Appl math model, 13, 47-57, (1989) · Zbl 0668.92017
[2] Ronghua, L.; Leung, P.; Pang, W., Convergence of numerical solutions to stochastic age-dependent population equations with Markovian switching, J comp appl math, 233, 1046-1055, (2009) · Zbl 1180.65008
[3] Wang, L.; Wang, X., Convergence of the semi-implicit Euler method for stochastic age-dependent population equations with Poisson jumps, Appl math model, 34, 2034-2043, (2010) · Zbl 1193.60089
[4] Pang, W.K.; Ronghua, L.; Min, L., Convergence of the semi-implicit Euler method for stochastic age-dependent population equations, Appl math comput, 195, 466-474, (2008) · Zbl 1159.65010
[5] Ronghua, L.; Pang, W.K.; Wang, Q., Numerical analysis for stochastic age-dependent population equations with Poisson jumps, J math anal appl, 327, 1214-1224, (2007) · Zbl 1115.65008
[6] Ronghua, Li; Wan-kai, Pang; Ping-kei, Leung, Convergence of numerical solutions to stochastic age-structured population equations with diffusions and Markovian switching, Appl math comput, 216, 744-752, (2010) · Zbl 1202.92072
[7] Ronghua, L.; Hongbing, Meng; Qin, Chang, Convergence of numerical solutions to stochastic age-dependent population equations, J comput appl math, 193, 109-120, (2006) · Zbl 1093.60046
[8] Zhang, Qi-min; Han, Chong-zhao, Numerical analysis for stochastic age-dependent population equations, Appl math comput, 169, 278-294, (2005) · Zbl 1088.65004
[9] Zhang, Qimin; Han, Chongzhao, Convergence of numerical solutions to stochastic age-structured population system with diffusion, Appl math comput, 186, 1234-1242, (2007) · Zbl 1123.65006
[10] Zhou, Shaobo; Wu, Fuke, Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching, J comput appl math, 229, 85-96, (2009) · Zbl 1168.65007
[11] A. Jensen, A distribution model applicable to economics. Munkgaard, Copenhagen, Denmark; 1954. · Zbl 0055.38005
[12] Zhang, H.; Basin, M.; Skliar, M., Optimal state estimation for continuous stochastic state-space system with hybrid measurements, Int J innovat comput control, 2, 370-457, (2006)
[13] Neuts, M.F., Probability distribution of phase type, (1975), Belgium Univ. of Louvain Belgium
[14] Anderson, W.J., Continuous-time Markov chains, (1991), Springer Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.