2005, 2005(Special): 463-475. doi: 10.3934/proc.2005.2005.463

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, Japan

2. 

Department of Mathematics, Faculty of Engineering, Musashi Institute of Technology, Tokyo 158-8557, Japan, Japan

3. 

Applied Mathematics Research Group, Graduate School of Engineering, Hiroshima 739-8527, Japan

Received  September 2004 Revised  June 2005 Published  September 2005

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.
Citation: S. Kanagawa, K. Inoue, A. Arimoto, Y. Saisho. Mean square approximation of multi dimensional reflecting fractional Brownian motion via penalty method. Conference Publications, 2005, 2005 (Special) : 463-475. doi: 10.3934/proc.2005.2005.463
[1]

Guolian Wang, Boling Guo. Stochastic Korteweg-de Vries equation driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5255-5272. doi: 10.3934/dcds.2015.35.5255

[2]

Vyacheslav M. Abramov, Fima C. Klebaner, Robert Sh. Lipster. The Euler-Maruyama approximations for the CEV model. Discrete & Continuous Dynamical Systems - B, 2011, 16 (1) : 1-14. doi: 10.3934/dcdsb.2011.16.1

[3]

Defei Zhang, Ping He. Functional solution about stochastic differential equation driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 281-293. doi: 10.3934/dcdsb.2015.20.281

[4]

Ahmed Boudaoui, Tomás Caraballo, Abdelghani Ouahab. Stochastic differential equations with non-instantaneous impulses driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2521-2541. doi: 10.3934/dcdsb.2017084

[5]

María J. Garrido–Atienza, Kening Lu, Björn Schmalfuss. Random dynamical systems for stochastic partial differential equations driven by a fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 473-493. doi: 10.3934/dcdsb.2010.14.473

[6]

Pavel Chigansky, Fima C. Klebaner. The Euler-Maruyama approximation for the absorption time of the CEV diffusion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (5) : 1455-1471. doi: 10.3934/dcdsb.2012.17.1455

[7]

Giacomo Dimarco. The moment guided Monte Carlo method for the Boltzmann equation. Kinetic & Related Models, 2013, 6 (2) : 291-315. doi: 10.3934/krm.2013.6.291

[8]

Jiakou Wang, Margaret J. Slattery, Meghan Henty Hoskins, Shile Liang, Cheng Dong, Qiang Du. Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow. Mathematical Biosciences & Engineering, 2006, 3 (4) : 683-696. doi: 10.3934/mbe.2006.3.683

[9]

Yong Xu, Rong Guo, Di Liu, Huiqing Zhang, Jinqiao Duan. Stochastic averaging principle for dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2014, 19 (4) : 1197-1212. doi: 10.3934/dcdsb.2014.19.1197

[10]

Yong Xu, Bin Pei, Rong Guo. Stochastic averaging for slow-fast dynamical systems with fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2257-2267. doi: 10.3934/dcdsb.2015.20.2257

[11]

Fuke Wu, Xuerong Mao, Peter E. Kloeden. Discrete Razumikhin-type technique and stability of the Euler--Maruyama method to stochastic functional differential equations. Discrete & Continuous Dynamical Systems - A, 2013, 33 (2) : 885-903. doi: 10.3934/dcds.2013.33.885

[12]

Jin Li, Jianhua Huang. Dynamics of a 2D Stochastic non-Newtonian fluid driven by fractional Brownian motion. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2483-2508. doi: 10.3934/dcdsb.2012.17.2483

[13]

Bahareh Akhtari, Esmail Babolian, Andreas Neuenkirch. An Euler scheme for stochastic delay differential equations on unbounded domains: Pathwise convergence. Discrete & Continuous Dynamical Systems - B, 2015, 20 (1) : 23-38. doi: 10.3934/dcdsb.2015.20.23

[14]

Yong Ren, Xuejuan Jia, Lanying Hu. Exponential stability of solutions to impulsive stochastic differential equations driven by $G$-Brownian motion. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2157-2169. doi: 10.3934/dcdsb.2015.20.2157

[15]

Shaokuan Chen, Shanjian Tang. Semi-linear backward stochastic integral partial differential equations driven by a Brownian motion and a Poisson point process. Mathematical Control & Related Fields, 2015, 5 (3) : 401-434. doi: 10.3934/mcrf.2015.5.401

[16]

Tyrone E. Duncan. Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5435-5445. doi: 10.3934/dcds.2015.35.5435

[17]

Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems & Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81

[18]

Janosch Rieger. The Euler scheme for state constrained ordinary differential inclusions. Discrete & Continuous Dynamical Systems - B, 2016, 21 (8) : 2729-2744. doi: 10.3934/dcdsb.2016070

[19]

Henryk Leszczyński, Monika Wrzosek. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion. Mathematical Biosciences & Engineering, 2017, 14 (1) : 237-248. doi: 10.3934/mbe.2017015

[20]

Wolf-Jüergen Beyn, Janosch Rieger. The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 409-428. doi: 10.3934/dcdsb.2010.14.409

 Impact Factor: 

Metrics

  • PDF downloads (0)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]