A Revisit of Stochastic Theta Method with some Improvements

Abstract

Considering the stochastic theta method, in this work we construct a modified solver for finding the solution of It$\hat{\text{o}}$ stochastic differential equations in the strong sense. It is discussed that the proposed variation is implicit with a better stability behavior as well as a higher order of convergence. Finally, the derived methods from the scheme are tested numerically to confirm their efficiency.