A boundary preserving numerical algorithm for the Wright-Fisher model with mutation (Q438725)

The paper is devoted to numerical integration of the equation \[ dY=(A-(A+B)Y)dt+\sqrt{Y(1-Y)}dw(t),\;A>0,\;B>0, \] describing the Wright-Fisher model. Any solution of the equation remains within the interval \([0,1]\) for all time. The authors propose a novel numerical method that ensures approximations remain within \([0,1]\) as well. Strong convergence of the method is proved. The method is extended to a multidimensional case.