Rooted tree analysis of the order conditions of row-type scheme for stochastic differential equations
The paper considers weak discrete time approximations for solutions of stochastic differential equations. The well-known rooted tree analysis developed by Butcher for ordinary differential equations is generalised to the case of stochastic differential equations. The roots are bi-colored corresponding to ordinary and stochastic integral terms. The order conditions are derived for the Rosenbrock-Wanner type numerical schemes. These are known to have good stability and efficiency properties. The analysis crucially involves the Stratonovich-Taylor expansion.
Rosenbrock-Wanner type numerical schemes
scientific article; zbMATH DE number 1000363
scientific article