TY - JOUR
TI - Cheap arbitrary high order methods for single integrand SDEs
LA - eng
AU - Debrabant, Kristian
AU - Kværnø, Anne
JF - Bit (lisse)
VL - 57
IS - 1
SP - 153
EP - 168
PY - 2017
SN - 15729125, 00063835
AB - For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order $p_d$ we obtain methods converging in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$. The reason is that the B-series of the exact solution and numerical approximation are, due to the single integrand and the usual rules of calculus holding for Stratonovich integration, similar to the ODE case. The only difference is that integration with respect to time is replaced by integration with respect to the measure induced by the single integrand SDE.
DO - 10.1007/s10543-016-0619-8
ER -