zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Exponential stability of numerical solutions to a stochastic age-structured population system with diffusion. (English) Zbl 1149.65009
Author’s summary: The main aim of this paper is to investigate the exponential stability of the Euler method for a stochastic age-structured population system with diffusion. The definition of exponential mean-square stability of a numerical method is introduced. It is proved that the Euler scheme is exponentially stable in mean square sense. An example is given for illustration.
65C30Stochastic differential and integral equations
60H35Computational methods for stochastic equations
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
92D25Population dynamics (general)
60H10Stochastic ordinary differential equations
34F05ODE with randomness
[1]Allen, L. J. S.; Thrasher, D. B.: The effects of vaccination in an age-dependent model for varicella and herpes zoster, IEEE trans. Automat. control 43, 779-789 (1998)
[2]Arnold, L.: Stochastic differential equations: theory and applications, (1972)
[3]Caraballo, T.; Real, J.: On the pathwise exponential stability of non-linear stochastic partial differential equations, Stochastic anal. Appl. 83, No. 5, 517-525 (1994) · Zbl 0808.93069 · doi:10.1080/07362999408809370
[4]Caraballo, T.; Liu, K.: On exponential stability criteria of stochastic partial differential equations, Stochastic process. Appl. 83, 289-301 (1999) · Zbl 0997.60065 · doi:10.1016/S0304-4149(99)00045-9
[5]Cushing, J. M.: The dynamics of hierarchical age-structured populations, J. math. Biol. 32, 705-729 (1994) · Zbl 0823.92018 · doi:10.1007/BF00163023
[6]Hernandez, E. Gaston: Age-density dependent population dispersal in RN, Math. biosci. 149, 37-56 (1998) · Zbl 0947.92026 · doi:10.1016/S0025-5564(97)10014-1
[7]Kloeden, P. E.; Platen, E.: Numerical solution of stochastic differential equations, (1992) · Zbl 0752.60043
[8]Mao, X.: Stochastic differential equations and applications, (1997)
[9]Marion, G.; Mao, X.; Renshaw, E.: Convergence of the Euler scheme for a class of stochastic differential equation, Internat. math. J. 1, No. 1, 9-22 (2002) · Zbl 0987.60068
[10]Platen, E.: An introduction to numerical methods for stochastic differential equations, Acta numerica 8, 197-246 (1999) · Zbl 0942.65004
[11]Pollard, J. H.: On the use of the direct matrix product in analyzing certain stochastic population model, Biometrika 53, 397-415 (1966) · Zbl 0144.43901
[12]Fister, K. Renee; Lenhart, S.: Optimal control of a competitive system with age-structure, J. math. Anal. appl. 291, 526-537 (2004) · Zbl 1043.92031 · doi:10.1016/j.jmaa.2003.11.031
[13]Ronghua, L.; Hongbing, M.; Qin, C.: Exponential stability of numerical solutions to sddes with Markovian switching, Appl. math. Comput. 174, No. 2, 1302-1313 (2006) · Zbl 1105.65010 · doi:10.1016/j.amc.2005.05.037
[14]Zhang, Q. -M.; Wen-An, L.; Zan-Kan, N.: Existence, uniqueness and exponential stability for stochastic age-dependent population, Appl. math. Comput. 154, 183-201 (2004) · Zbl 1051.92033 · doi:10.1016/S0096-3003(03)00702-1
[15]Zhang, Q. M.; Zhao, H. Chong: Numerical analysis for stochastic age-dependent population equations, Appl. math. Comput. 176, 210-223 (2005)