Introduction to the numerical analysis of stochastic delay differential equations

Journal of Computational and Applied Mathematics

Volumn 125, Issue 1-2, 2000, Pages 297-307

  Buckwar, Evelyn ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; RANDOM PROCESSES; THEOREM PROVING;

EULER-MARUYAMA SCHEME; STOCHASTIC DELAY DIFFERENTIAL EQUATIONS (SDDE);

DIFFERENTIAL EQUATIONS;

EID: 0034509078     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00475-1     Document Type: Article

References (14)

1. L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley-Interscience, New York, 1974.
2. C.T.H. Baker, E. Buckwar, Introduction to the numerical analysis of stochastic delay differential equations, MCCM Numerical Analysis Technical Report, Manchester University, ISSSN 1360-1725, 1999.
3. A. Beuter, J. Bélair, Feedback and delays in neurological diseases: a modelling study using dynamical systems, Bull. Math. Biol. 55 (3) (1993) 525-541.
4. J.M.C. Clark, The discretization of stochastic differential equations: a primer, in: H. Neunzert (Ed.), Road Vehicle Systems and Related Mathematics; Proceedings of the second DMV-GAMM Workshop, Torino, 1987, Teubner, Stuttgart, and Kluwer Academic Publishers, Amsterdam, pp. 163-179.
5. R.D. Driver, Ordinary and Delay Differential Equations, Applied Mathematical Sciences, Vol. 20, Springer, New York, 1977.
6. C.W. Eurich, J.G. Milton, Noise-induced transitions in human postural sway, Phys. Rev. E 54 (6) (1996) 6681-6684.
7. I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York, 1991.
8. P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
9. M.C. Mackey, A. Longtin, J.G. Milton, J.E. Bos, Noise and critical behaviour of the pupil light reflex at oscillation onset, Phys. Rev. A 41 (12) (1990) 6992-7005.
10. X. Mao, Stochastic Differential Equations and their Applications, Horwood Publishing Limited, Chichester, 1997.
11. G.N. Milstein, Numerical Integration of Stochastic Differential Equations, Kluwer Academic Publishers, Dordrecht, 1995 (Translated and revised from the 1988 Russian original.)
12. S.E.A. Mohammed, Stochastic Functional Differential Equations, Pitman (Advanced Publishing Program), Boston, MA, 1984.
13. D. Williams, Probability with Martingales, Cambridge University Press, Cambridge, 1991.
14. M. Zennaro, Delay differential equations: theory and numerics, in: M. Ainsworth, J. Levesley, W.A. Light, M. Marletta (Eds.), Theory and Numerics of Ordinary and Partial Differential Equations (Leicester, 1994), Oxford University Press, New York, 1995, pp. 291-333.