Hernán Mardones, Carlos M. Mora:
First-order weak balanced schemes for bilinear stochastic differential equations
This paper starts to develop balanced schemes for stochastic differential equations (SDEs) with multiplicative noise based on the addition of stabilizing functions to the drift terms. First, we use the linear scalar SDE as a test problem to show that it is possible to construct efficient almost sure stable first-order weak balanced schemes. Second, we design balanced schemes for bilinear SDEs that achieve the first order of weak convergence, and do not involve the simulation of multiple stochastic integrals. Numerical experiments show a promising performance of the new numerical methods.