TY - JOUR
T1 - Conservative Methods for Stochastic Differential Equations with a Conserved Quantity
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 435
EP - 456
PY - 2016
DA - 2016/05
SN - 13
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/447.html
KW - Stochastic differential equations, invariants, conservative methods, stochastic geometric numerical integration, quadrature formula, splitting technique, mean-square convergence order, weak convergence order.
AB - <p style="text-align: justify;">This paper proposes a novel conservative method for the numerical approximation
of general stochastic differential equations in the Stratonovich sense with a conserved quantity.
We show that the mean-square order of the method is 1 if noises are commutative and that the
weak order is 1 in the general case. Since the proposed method may need the computation of a
deterministic integral, we analyse the effect of the use of quadrature formulas on the convergence
orders. Furthermore, based on the splitting technique of stochastic vector fields, we construct
conservative composition methods with similar orders as the above method. Finally, numerical
experiments are presented to support our theoretical results.</p>