Approximation of some stochastic differential equations by the splitting up method (Q1186093)

This paper considers approximation schemes for the solution of the stochastic initial value problem \(dy(t)+A(t,y(t))dt=B(t,y(t))dW(t)\), \(t\in [0,T]\), \(y(0)=y_ 0\). These schemes arise by splitting up the stochastic differential equation as \(d\varphi+A(t,\varphi)dt=0\), \(d\psi=B(t,\psi)dW\). After sufficient hypotheses are identified, convergence of the schemes is proved and error bounds are established. The paper concludes by presenting the methods which result when the schemes are applied to the Zaklaï equation.