On a type of stochastic differential equations driven by countably many Brownian motions

被引：41

作者：

Cao, GL ^{[1
]}

He, K ^{[1
]}

机构：

[1] Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Hubei, Peoples R China

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2003年 / 203卷 / 01期

关键词：

one-dimensional SDE; existence; uniqueness; non-contact property; strong comparison theorem;

D O I：

10.1016/S0022-1236(03)00066-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Consider the one-dimensional SDE X-t = x+ Sigma(i=1)(infinity) integral(0)(1)sigma(i)(X-s) dW(s)(i) + integral(0)(1)b(X-s) ds, where W-i is an infinite sequence of independent standard Brownian motions, i = 1, 2, 3,... . We prove two theorems on the existence and uniqueness of solutions with non-Lipschitz coefficients, and give a non-contact property and a strong comparison theorem for solutions. (C) 2003 Elsevier Science (USA). All rights reserved.

引用

页码：262 / 285

页数：24

共 14 条

[1] Modulus of continuity of the canonic Brownian motion "on the group of diffeomorphisms of the circle" [J].

Airault, H ;

Ren, JG .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 196 (02) :395-426

[2]

[Anonymous], LECT NOTES MATH

[3]

[Anonymous], 1997, STOCHASTIC PROCESS A

[4]

Gong G., 2000, INTRO STOCHASTIC DIF

[5]

HUANG ZY, 2000, FDN STOCHASTIC ANAL

[6]

LEGALL JF, 1983, LECT NOTES MATH, V986, P15

[7] Existence and pathwise uniqueness of solutions for stochastic differential equations with respect to martingales in the plane [J].

Liang, ZX .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1999, 83 (02) :303-317

[8] On the existence and uniqueness of solutions to stochastic differential equations of mixed Brownian and Poissonian sheet type [J].

Liu, JC .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 94 (02) :339-354

[9] The canonic diffusion above the diffeomorphism group of the circle [J].

Malliavin, P .

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (04) :325-329

[10] ADAPTED SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL-EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS [J].

MAO, XR .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1995, 58 (02) :281-292

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