DISCRETIZATION ERROR IN SIMULATION OF ONE-DIMENSIONAL REFLECTING BROWNIAN MOTION

被引：85

作者：

Asmussen, Soren ^{[1
]}

Glynn, Peter ^{[2
]}

Pitman, Jim ^{[3
]}

机构：

[1] Univ Aalborg, Inst Elect Syst, DK-9220 Aalborg, Denmark

[2] Stanford Univ, Dept Operat Res, Stanford, CA 94305 USA

[3] Univ Calif Berkeley, Dept Stat, Berkeley, CA 94720 USA

来源：

ANNALS OF APPLIED PROBABILITY | 1995年 / 5卷 / 04期

关键词：

Bessel bridge; Bessel process; bias; excursion; Euler scheme; path decomposition; Riemann zeta function; Spitzer's identity; stochastic differential equation;

D O I：

10.1214/aoap/1177004597

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

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.

引用

页码：875 / 896

页数：22

共 38 条

[1]

Abramowitz M.., 1972, HDB MATH FUNCTIONS

[2]

[Anonymous], 1940, COMPOS MATH, DOI DOI 10.1080/17442508508833361

[3] QUEUING SIMULATION IN HEAVY TRAFFIC [J].

ASMUSSEN, S .

MATHEMATICS OF OPERATIONS RESEARCH, 1992, 17 (01) :84-111

[4]

ASMUSSEN S, 1989, STOCH MODELS, V5, P617

[5]

Asmussen S., 1987, APPL PROBABILITY QUE

[6]

Barlow R., 1981, STAT THEORY RELIABIL

[7]

BIANE P, 1988, B SCI MATH, V112, P101

[8]

Bratley P, 1987, GUIDE SIMULATION, V2nd

[9]

CALVIN J. M, 1992, AVERAGE PERFORMANCE

[10]

Chitashvili R.J., 1981, STOCHASTICS, V5, P225

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