DISCRETIZATION ERROR IN SIMULATION OF ONE-DIMENSIONAL REFLECTING BROWNIAN MOTION
成果类型：
Article
署名作者：
Asmussen, Soren; Glynn, Peter; Pitman, Jim
署名单位：
Aalborg University; Stanford University; University of California System; University of California Berkeley
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004597
发表日期：
1995
页码：
875-896
关键词：
摘要：
This paper is concerned with various aspects of the simulation of one-dimensional reflected (or regulated) Brownian motion. The main result shows that the discretization error associated with the Euler scheme for simulation of such a process has both a strong and weak order of convergence of precisely 1/2. This contrasts with the faster order 1 achievable for simulations of SDE's without reflecting boundaries. The asymptotic distribution of the discretization error is described using Williams' decomposition of a Brownian path at the time of a minimum. Improved methods for simulation of reflected Brownian motion are discussed.