A FUNDAMENTAL MEAN-SQUARE CONVERGENCE THEOREM FOR SDEs WITH LOCALLY LIPSCHITZ COEFFICIENTS AND ITS APPLICATIONS

作者：Tretyakov, M. V.^*; Zhang, Z.

来源：SIAM Journal on Numerical Analysis, 2013, 51(6): 3135-3162.

DOI：10.1137/120902318

• SDEs with nonglobally Lipschitz coefficients
• numerical integration of SDEs in the mean-square sense
• balanced methods
• fully implicit methods
• strong convergence
• almost sure convergence

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDEs) in which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The theorem is illustrated on a number of particular numerical methods, including a special balanced scheme and fully implicit methods. The proposed special balanced scheme is explicit and its mean-square order of convergence is 1/2. Some numerical tests are presented.

• 出版日期2013