Adaptive Euler methods for stochastic systems with non-globally Lipschitz coefficients

Abstract We present strongly convergent explicit and semi-implicit adaptive numerical schemes for systems of semi-linear stochastic differential equations (SDEs) where both the drift diffusion are not globally Lipschitz continuous. Numerical instability may arise either from stiffness linear operator or perturbation nonlinear under discretization, both. Typical applications space discretization an SPDE, volatility models in finance, certain ecological models. Under conditions that include montonicity, we prove a timestepping strategy which adapts stepsize based on alone is sufficient to control growth obtain strong convergence with polynomial order. The order our scheme (1 − ε )/2, ∈ (0,1), becomes arbitrarily small as number finite moments available solutions SDE increases. Numerically, compare method fully drift-implicit three other methods. Our results show overall robust, efficient, well suited general purpose solver.