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Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift. (English) Zbl 1246.65010
Under less restrictive assumptions on the drift coefficient $$f$$ than is customary, the split-step backward Euler method is shown to converge strongly with order $$1/2$$ to the solution of the Ito stochastic differential equation $dX(t)= f(t,X(t))\,dt+ g(t,X(r))\,dW(t),\quad 0\leq t\leq T,\quad X(0)= X_0.$ Numerical results are presented that verify that this accuracy is achieved for three examples. Also under even less restrictive assumptions on $$f$$ , order $$1/4$$ strong convergence to the solution is proved.

##### MSC:
 65C30 Numerical solutions to stochastic differential and integral equations 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H35 Computational methods for stochastic equations (aspects of stochastic analysis) 34F05 Ordinary differential equations and systems with randomness 65L05 Numerical methods for initial value problems 65L20 Stability and convergence of numerical methods for ordinary differential equations
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