an:06027490
Zbl 1246.65010
Bastani, Ali Foroush; Tahmasebi, Mahdieh
Strong convergence of split-step backward Euler method for stochastic differential equations with non-smooth drift
EN
J. Comput. Appl. Math. 236, No. 7, 1903-1918 (2012).
00295441
2012
j
65C30 60H10 60H35 34F05 65L05 65L20
stochastic differential equations; non-smooth drift; split-step backward Euler method; Euler; Maruyama method; one-sided Lipschitz condition; convergence; Ito stochastic differential equation; numerical results
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.
Melvin D. Lax (Long Beach)