A Second Order Weak Approximation of SDEs Using Markov Chain Without Levy Area Simulation

Abstract

This paper proposes a new Markov chain approach to second order weak approximation of stochastic differential equations driven by d-dimensional Brownian motion. The scheme is explicitly constructed by polynomials of Brownian motions up to second order and any discrete moment matched random variables or Levy area simulation method are not used. The number of required random variables is still d in one-step simulation on the implementation of the scheme. In the Markov chain, a correction term with Lie bracket of vector fields associated with SDEs appears as the cost of not using moment matched random variables.