WEAK CONVERGENCE OF A NUMERICAL SCHEME FOR STOCHASTIC
Abstract: In this paper a numerical scheme approximating the solution to a stochastic differential
equation is presented. On bounded subsets of time, this scheme has a finite state space, which
allows us to decrease the round-off error when the algorithm is implemented. At the same
time, the scheme introduced turns out locally consistent for any step size of time. Weak
convergence of the scheme to the solution of the stochastic differential equation is shown.
2010 AMS Mathematics Subject Classification: Primary: 60G99; Secondary:
Keywords and phrases: Numerical methods, round-off error, stochastic differential
equations, weak convergence.