Two-Sided Error Estimates for the Stochastic Theta Method

Beyn W-J, Kruse R (2010)
Discrete and Continuous Dynamical Systems -Series B 14(2): 389-407.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
Two-sided error estimates are derived for the strong error of convergence of the stochastic theta method. The main result is based on two ingredients. The first one shows how the theory of convergence can be embedded into standard concepts of consistency, stability and convergence by an appropriate choice of norms and function spaces. The second one is a suitable stochastic generalization of Spijker's norm (1968) that is known to lead to two-sided error estimates for deterministic one-step methods. We show that the stochastic theta method is bistable with respect to this norm and that well-known results on the optimal O(root h) order of convergence follow from this property in a natural way.
Stichworte
SODE; bistability; stochastic theta method; stochastic Spijker norm; two-sided error estimate; consistency
Erscheinungsjahr
2010
Zeitschriftentitel
Discrete and Continuous Dynamical Systems -Series B
Band
14
Ausgabe
2
Seite(n)
389-407
ISSN
1531-3492
Page URI
https://pub.uni-bielefeld.de/record/1795449

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Beyn W-J, Kruse R. Two-Sided Error Estimates for the Stochastic Theta Method. Discrete and Continuous Dynamical Systems -Series B. 2010;14(2):389-407.
Beyn, W. - J., & Kruse, R. (2010). Two-Sided Error Estimates for the Stochastic Theta Method. Discrete and Continuous Dynamical Systems -Series B, 14(2), 389-407. doi:10.3934/dcdsb.2010.14.389
Beyn, W. - J., and Kruse, R. (2010). Two-Sided Error Estimates for the Stochastic Theta Method. Discrete and Continuous Dynamical Systems -Series B 14, 389-407.
Beyn, W.-J., & Kruse, R., 2010. Two-Sided Error Estimates for the Stochastic Theta Method. Discrete and Continuous Dynamical Systems -Series B, 14(2), p 389-407.
W.-J. Beyn and R. Kruse, “Two-Sided Error Estimates for the Stochastic Theta Method”, Discrete and Continuous Dynamical Systems -Series B, vol. 14, 2010, pp. 389-407.
Beyn, W.-J., Kruse, R.: Two-Sided Error Estimates for the Stochastic Theta Method. Discrete and Continuous Dynamical Systems -Series B. 14, 389-407 (2010).
Beyn, Wolf-Jürgen, and Kruse, Raphael. “Two-Sided Error Estimates for the Stochastic Theta Method”. Discrete and Continuous Dynamical Systems -Series B 14.2 (2010): 389-407.