A Strongly Monotonic Polygonal Euler Scheme

Rate of convergence results are presented for a new class of explicit Euler schemes, which approximate stochastic differential equations (SDEs) with superlinearly growing drift coefficients that satisfy a particular form of strong monotonicity. The new, distinct feature of this class of explicit schemes is the preservation of the monotonicity condition for the new, suitably controlled drift coefficients that guaranty the finiteness of moments of the numerical solutions up to a desired order.