Mean-square stability of numerical schemes for stochastic differential systems

Taketomo Mitsui

Graduate School of Human Informatics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

tom.mitsui@cc.nagoya-u.ac.jp

http://www.math.human.nagoya-u.ac.jp/~mitsui/index-e.html

Poster

Stochastic differential equations (SDEs) represent physical phenomena dominated by stochastic processes. Similar to deterministic ordinary differential equations (ODEs), various numerical schemes are proposed for SDEs. Stability analysis is significant for numerical SDEs as well, however a few results have been known. We have proposed the mean-square stability of numerical schemes for a scalar SDE, that is, the numerical stability with respect to the mean-square norm. We studied it, however, only for scalar SDEs because of difficulty and complexity in SDE systems. Trying to make a breakthrough, we will consider a 2-dimensional linear system with one multiplicative noise and give stability criteria under several notions of the matrix norm. This is a joint work with Yoshihiro Saito.