We propose two new positive weak second-order approximations for the CIR equation dXt=(a−bXt)dt+σXtdBt based on splitting, at each step, the equation into the deterministic part dXt=(a−bXt)dt, which is solved exactly, and the stochastic part dXt=σXtdBt, which is approximated in...

We consider scalar stochastic differential equations of the formdXt=μ(Xt)dt+σ(Xt)dBt,X0=x0,where B is a standard Brownian motion. Suppose that the coefficients are such that the solution X possesses the (a, b)-invariance property for some interval (a,b)⊂R:Xt∈(a,b) for all t≥0 if...