Exponential timestepping with boundary test for stochastic differential equations

SIAM Journal on Scientific Computing

Volumn 24, Issue 5, 2003, Pages 1809-1822

  Jansons, Kalvis M ^a   Lythe, G D ^b,c  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

^c UNIVERSITY OF LEEDS   (United Kingdom)

Author keywords

A posteriori error estimates; Diffusion with boundaries; Numerical methods; Stochastic calculus

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); ERROR ANALYSIS; ESTIMATION;

A POSTERIORI ERROR ESTIMATES; BOUNDARY TESTS; EXPONENTIAL TIMESTEPPING; STOCHASTIC DIFFERENTIAL EQUATIONS;

RANDOM PROCESSES;

EID: 0141906255     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827501399535     Document Type: Article

References (21)

1. A. Greiner, W. Strittmatter, and J. Honerkamp, Numerical integration of stochastic differential equations, J. Statist. Phys., 51 (1988), pp. 95-108.
2. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, 1992.
3. K. Burrage and P. M. Burrage, High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numer. Math., 22 (1996), pp. 91-107.
4. R. Mannella, Numerical tricks for studying large rare fluctuations, J. Physique, 8 (1998), pp. 241-245.
5. E. Platen, An introduction to numerical methods for stochastic differential equations, Acta Numer., 8 (1999), pp. 195-244.
6. D. J. Higham, An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, SIAM Rev., 43 (2001), pp. 525-546.
7. K. M. Jansons and G. D. Lythe, Efficient numerical solution of stochastic differential equations using exponential timestepping, J. Statist. Phys., 100 (2000), pp. 1097-1109.
8. P. Baldi, Exact asymptotics for the probability of exit from a domain and applications to simulation, Ann. Prob., 23 (1995), pp. 1644-1670.
9. G. N. Milstein and M. V. Tretyakov, Simulation of a space-time bounded diffusion, Ann. Appl. Probab., 9 (1999), pp. 732-779.
10. R. Mannella, Boundaries and optimal stopping in a stochastic differential equation, Phys. Lett. A, 254 (1999), pp. 257-262.
11. E. Gobet, Weak approximation of killed diffusion using Euler schemes, Stochastic Process. Appl., 87 (2000), pp. 167-197.
12. K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer, Berlin, 1974.
13. L. C. G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales. Vol 2: Itô Calculus, John Wiley, Chichester, UK, 1987.
14. A. N. Borodin and P. Salminen, Handbook of Brownian Motion-Facts and Formulae, Birkhäuser, Basel, 1996.
15. S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, Orlando, 1981.
16. K. M. Jansons and G. D. Lythe, Stochastic calculus: Application to dynamic bifurcations and threshold crossings, J. Statist. Phys., 90 (1998), pp. 227-251.
17. C. W. Gardiner, Handbook of Stochastic Methods, Springer, Berlin, 1985.
18. C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, 1978.
19. J. D. Murray, Asymptotic Analysis, Springer, New York, 1984.
20. M. Seeßelberg and F. Petruccione, An improved algorithm for the estimation of the mean first passage time of ordinary stochastic differential equations, Comput. Phys. Comm., 74 (1993), pp. 247-255.
21. M. Beccaria, G. Curci, and A. Viceré, Numerical solutions of first-exit-time problems, Phys. Rev. E, 48 (1993), pp. 1539-1546.