Stability analysis of numerical schemes for stochastic differential equations

被引：291

作者：

Saito, Y ^{[1
]}

Mitsui, T ^{[1
]}

机构：

[1] NAGOYA UNIV,GRAD SCH HUMAN INFORMAT,CHIKUSA KU,NAGOYA,AICHI 46401,JAPAN

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 1996年 / 33卷 / 06期

关键词：

stochastic differential equations; numerical schemes; numerical stability;

D O I：

10.1137/S0036142992228409

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Stochastic differential equations (SDEs) represent physical phenomena dominated by stochastic processes. As for deterministic ordinary differential equations (ODEs), various numerical schemes are proposed for SDEs. In this paper we study the stability of numerical schemes for scalar SDEs with respect to the mean-square norm, which we call MS-stability. We will show some figures of the MS-stability domain or regions for some numerical schemes and present numerical results which confirm it. This notion is an extension of absolute stability in numerical methods for ODEs.

引用

页码：2254 / 2267

页数：14

共 24 条

[1]

[Anonymous], 1993, WORLD SCI SER APPL A

[2]

Arnold L., 1974, Stochastic Differential Equations: Theory and Applications, DOI DOI 10.1002/ZAMM.19770570413

[3]

ARTEMIEV SS, 1996, B NOV COMPUT CTR NUM, V1, P1

[4]

Gard T.C., 1988, INTRO STOCHASTIC DIF

[5] A-STABILITY OF RUNGE-KUTTA METHODS FOR SYSTEMS WITH ADDITIVE NOISE [J].

HERNANDEZ, DB ;

SPIGLER, R .

BIT, 1992, 32 (04) :620-633

[6] NUMERICAL-INTEGRATION OF MULTIPLICATIVE-NOISE STOCHASTIC DIFFERENTIAL-EQUATIONS [J].

KLAUDER, JR ;

PETERSEN, WP .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1985, 22 (06) :1153-1166

[7] THE NUMERICAL SOLUTION OF NONLINEAR STOCHASTIC DYNAMICAL SYSTEMS: A BRIEF INTRODUCTION [J].

Kloeden, P. E. ;

Platen, E. ;

Schurz, H. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1991, 1 (02) :277-286

[8] HIGHER-ORDER IMPLICIT STRONG NUMERICAL SCHEMES FOR STOCHASTIC DIFFERENTIAL-EQUATIONS [J].

KLOEDEN, PE ;

PLATEN, E .

JOURNAL OF STATISTICAL PHYSICS, 1992, 66 (1-2) :283-314

[9] A SURVEY OF NUMERICAL-METHODS FOR STOCHASTIC DIFFERENTIAL-EQUATIONS [J].

KLOEDEN, PE ;

PLATEN, E .

STOCHASTIC HYDROLOGY AND HYDRAULICS, 1989, 3 (03) :155-178

[10]

Kloeden PE, 2011, Stochastic differential equations

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