Abstract
In this paper, we construct a new split-step method for solving stochastic differential equations, namely the split-step θ-method. Under Lipschitz and linear growth conditions, we establish a mean-square convergence theory of split-step θ-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 θ-method.
| Original language | English |
|---|---|
| Pages (from-to) | 1310-1321 |
| Number of pages | 12 |
| Journal | Computers and Mathematics with Applications |
| Volume | 60 |
| Issue number | 5 |
| DOIs | |
| State | Published - Sep 2010 |
| Externally published | Yes |
Keywords
- Mean-square convergence
- Mean-square stability
- Split-step θ-method
- Stochastic differential equations
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