On the approximations of solutions to stochastic differential equations under polynomial condition

The subject of this paper is an analytic approximate method for a class stochastic differential equations with coefficients that do not necessarily satisfy the Lipschitz and linear growth conditions but behave like polynomials. More precisely, from observed have unique solutions bounded moments their polynomial condition. Approximate are defined on partitions time interval, Taylor approximations initial equation. rate Lp convergence increases when degrees in increase. At end paper, example provided to support main theoretical result.