Seminar on Probability and Statistics

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Organizer(s) Nakahiro Yoshida, Teppei Ogihara, Yuta Koike

2016/10/31

11:30-12:20   Room #123 (Graduate School of Math. Sci. Bldg.)
Nobuaki Naganuma (Osaka University)
Error analysis for approximations to one-dimensional SDEs via perturbation method
[ Abstract ]
We consider one-dimensional stochastic differential equations driven by fractional Brownian motions and adopt the Euler scheme, the Milstein type scheme and the Crank-Nicholson scheme to approximate solutions to the equations. We introduce perturbation method in order to analyze errors of the schemes. By using this method, we can express the errors in terms of directional derivatives of the solutions explicitly. We obtain asymptotic error distributions of the three schemes by combining the expression of the errors and the fourth moment theorem. This talk is based on a joint work with Prof. Shigeki Aida (Tohoku University).