統計数学セミナー
Seminar on Probability and Statistics |
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Seminar on Probability and Statistics Wednesday December 22 2004 Tokyo 128 5:30-6:40 pm
Approximation of Reflecting Fractional Brownian Motion by Penalty Method
and its Applications
金川 秀也 / KANAGAWA, Shuya 武蔵工業大学, 工学部 / Musashi Institute of Technology Abstract We investigate the error of Euler-Maruyama approximate solution of
reflecting fractional Brownian motion with some boundary conditions on multi
dimensional domains(so-called Skorohod SDE) using the penalty method.
The fractional Brownian motion is applied in many fields including mathematical finance.
Forthe purpose of observing numerical data by computer simulation of Skorohod SDE
we define discretized approximate solution of the SDE and obtain its error estimation.
The penalty method is separated into two steps. The first step is to approximate
reflecting fractional Brownian motions by usual fractional Brownian motion with a drift
term whose coefficients are gradient type in pathwise sense.
The second step is to approximate the fractional Brownian motion with such
drift term by Euler-Maruyama scheme.
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