Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method

S. Kanagawa; K. Inoue; A. Arimoto; Y. Saisho

doi:10.3934/proc.2005.2005.463

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2005, Volume 2005: 463-475. Doi: 10.3934/proc.2005.2005.463 open access

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Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method

1.
Department of Mathematics, Faculty of Engineering, Musashi Institute of Technology, Tokyo, 158-8557
2.
Department of Mathematics, Faculty of Engineering, Musashi Institute of Technology, Tokyo 158-8557
3.
Applied Mathematics Research Group, Graduate School of Engineering, Hiroshima 739-8527

Received: August 31, 2004

Revised: May 31, 2005

Published: August 2005

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Abstract

We investigate the mean square error of the Euler-Maruyama type approximate solution of multi dimensional reflecting fractional Brownian motion using the penalty method. Furthermore we show some examples of the reflecting fractional Brownian motion with several boundaries.

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Mathematics Subject Classification: Primary: 60G50, 60H10; Secondary: 65C30.

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