A revisit to W2n-theory of super-parabolic backward stochastic partial differential equations in Rd

被引：28

作者：

Du, Kai ^{[1
]}

Meng, Qingxin ^{[1
,2
]}

机构：

[1] Fudan Univ, Sch Math Sci, Dept Finance & Control Sci, Shanghai 200433, Peoples R China

[2] Huzhou Teacher Coll, Dept Math Sci, Huzhou 31300, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 10期

关键词：

Backward stochastic partial differential equations; Cauchy problems; Sobolev spaces; ADAPTED SOLUTION; CONTROLLABILITY; SPDE;

D O I：

10.1016/j.spa.2010.06.001

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：

Backward stochastic partial differential equations of parabolic type with variable coefficients are considered in the whole Euclidean space. Improved existence and uniqueness results are given in the Sobolev space H-n (=W-2(n)) under weaker assumptions than those used by X. Zhou [X. Zhou, A duality analysis on stochastic partial differential equations, J. Funct. Anal. 103 (1992) 275-293]. As an application, a comparison theorem is obtained. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1996 / 2015

页数：20

共 23 条

[1] Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications [J].

Al-Hussein, AbdulRahman .

STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2009, 81 (06) :601-626

[2] Carleman estimates and controllability of linear stochastic heat equations [J].

Barbu, V ;

Rascanu, A ;

Tessitore, G .

APPLIED MATHEMATICS AND OPTIMIZATION, 2003, 47 (02) :97-120

[3]

Bensoussan A., 1983, Stochastics, V9, P169, DOI 10.1080/17442508308833253

[4]

Da Prato G, 1992, STOCHASTIC EQUATIONS

[5] Backward stochastic differential equations in finance [J].

El Karoui, N ;

Peng, S ;

Quenez, MC .

MATHEMATICAL FINANCE, 1997, 7 (01) :1-71

[6] UTILITY MAXIMIZATION WITH HABIT FORMATION: DYNAMIC PROGRAMMING AND STOCHASTIC PDEs [J].

Englezos, Nikolaos ;

Karatzas, Ioannis .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2009, 48 (02) :481-520

[7] On semi-linear degenerate backward stochastic partial differential equations [J].

Hu, Y ;

Ma, J ;

Yong, JM .

PROBABILITY THEORY AND RELATED FIELDS, 2002, 123 (03) :381-411

[8]

HU Y, 1991, STOCH ANAL APPL, V9, P445, DOI DOI 10.1080/07362999108809250

[9]

KRYLOV N. V., 1981, Journal of Soviet mathematics, V14, P1233

[10] On linear, degenerate backward stochastic partial differential equations [J].

Ma, J ;

Yong, JM .

PROBABILITY THEORY AND RELATED FIELDS, 1999, 113 (02) :135-170

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