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

21 Pages Posted: 23 Oct 2018

See all articles by Toshihiro Yamada

Toshihiro Yamada

Hitotsubashi University

Kenta Yamamoto

Bank of Tokyo-Mitsubishi, Ltd.

Date Written: September 28, 2018

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.

Suggested Citation

Yamada, Toshihiro and Yamamoto, Kenta, A Second Order Weak Approximation of SDEs Using Markov Chain Without Levy Area Simulation (September 28, 2018). Available at SSRN: https://ssrn.com/abstract=3257365 or http://dx.doi.org/10.2139/ssrn.3257365

Toshihiro Yamada (Contact Author)

Hitotsubashi University ( email )

2-1 Naka Kunitachi-shi
Tokyo 186-8601
Japan

Kenta Yamamoto

Bank of Tokyo-Mitsubishi, Ltd. ( email )

Japan

Register to save articles to
your library

Register

Paper statistics

Downloads
9
Abstract Views
86
PlumX Metrics