Preservation of probabilistic laws through Euler methods for ornstein-uhlenbeck process
作者:
Henri Schurz,
期刊:
Stochastic Analysis and Applications
(Taylor Available online 1999)
卷期:
Volume 17,
issue 3
页码: 463-486
ISSN:0736-2994
年代: 1999
DOI:10.1080/07362999908809613
出版商: Marcel Dekker, Inc.
关键词: Stochastic Differential Equations;Implicit Euler Methods;Stability
数据来源: Taylor
摘要:
There is a lack of appropriate replication of the asymptotical behaviour of stationary stochastic differential equations solved by numerical methods. The paper illustrates this fact with the stationary Ornstein-Uhlenbeck process and family of implicit Euler methods. For description of occuring bias, notions of asymptoticalp-th. mean, mean, mean square and equilibrium preservation are introduced, due to stochasticity of stationary law. Only the trapezoidal formula among these methods is optimal in the sense of replication of exact asymptotical behaviour. We also discuss the general probabilistic law of linear Euler methods. The results can be useful for implementation of stochastic-numerical algorithms (e.g. for linear-implicit methods) in several disciplines of Natural and Environmental Sciences
点击下载:
PDF (765KB)
返 回