Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 60, Issue 5, Pages 1310-1321Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.06.011
Keywords
Stochastic differential equations; Split-step theta-method; Mean-square convergence; Mean-square stability
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Funding
- National Natural Science Foundation of China [10671047]
- Foundation of HITC [200713]
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In this paper, we construct a new split-step method for solving stochastic differential equations, namely the split-step theta-method. Under Lipschitz and linear growth conditions, we establish a mean-square convergence theory of split-step theta-approximate solutions. Moreover, the mean-square stability of the method for a linear test equation with real parameters is considered and the real mean-square stability region is plotted. Finally, numerical results are presented to demonstrate the efficiency of the split-step theta-method. (C) 2010 Elsevier Ltd. All rights reserved.
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