A-stability and Stochastic Mean-square Stability

BIT Numerical Mathematics

Volumn 40, Issue 2, 2000, Pages 404-409

  Higham, Desmond J ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Mean square; Milstein method; Multiplicative noise; Theta method

Indexed keywords

EID: 0042185223     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022355410570     Document Type: Article

References (9)

1. S. S. Artemiev and T. A. Averina, Numerical Analysis of Systems of Ordinary and Stochastic Differential Equations, VSP, Utrecht, 1997.
2. E. Hairer and G. Wanner, Solving Ordinary Differential Equations II, Stiff and Differential-Algebraic Problems, 2nd ed., Springer Verlag, Berlin, 1996.
3. D. B. Hernandez and R. Spigler, A-stability of Runge-Kutta methods for systems with additive noise, BIT, 32 (1992), pp. 620-633.
4. D. J. Higham, Mean-square and asymptotic stability of the stochastic theta method, SIAM J. Numer. Anal., to appear.
5. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer-Verlag, Berlin, 1992.
6. J. D. Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley, Chichester, 1991.
7. X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, 1997.
8. E. Platen, An introduction to numerical methods for stochastic differential equations, Acta Numerica, 8 (1999), pp. 197-246.
9. Y. Saito and T. Mitsui, Stability analysis of numerical schemes for stochastic differential equations, SIAM J. Numer. Anal., 33 (1996), pp. 2254-2267.