Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space II

被引：13

作者：

Barbu, Viorel ^{[1
,2
]}

Da Prato, Giuseppe ^{[3
]}

Tubaro, Luciano ^{[4
]}

机构：

[1] Alexandru Ioan Cuza Univ, Iasi 700506, Romania

[2] Inst Math Octav Mayer, Iasi 700506, Romania

[3] Scuola Normale Super Pisa, I-56126 Pisa, Italy

[4] Univ Trento, Dept Math, I-38050 Povo, Trento, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2011年 / 47卷 / 03期

关键词：

Neumann problem; Ornstein-Uhlenbeck operator; Kolmogorov operator; Reflection problem; Infinite-dimensional analysis; SPDES;

D O I：

10.1214/10-AIHP381

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 work is concerned with the existence and regularity of solutions to the Neumann problem associated with a Ornstein-Uhlenbeck operator on a bounded and smooth convex set K of a Hilbert space H. This problem is related to the reflection problem associated with a stochastic differential equation in K.

引用

页码：699 / 724

页数：26

共 16 条

[1] Existence and stability for Fokker-Planck equations with log-concave reference measure [J].

Ambrosio, Luigi ;

Savare, Giuseppe ;

Zambotti, Lorenzo .

PROBABILITY THEORY AND RELATED FIELDS, 2009, 145 (3-4) :517-564

[2]

[Anonymous], 1998, GAUSSIAN MEASURES

[3]

[Anonymous], 2002, LONDON MATH SOC LECT

[4] The Neumann problem on unbounded domains of Rd and stochastic variational inequalities [J].

Barbu, V ;

Da Prato, G .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2005, 30 (08) :1217-1248

[5] The generator of the transition semigroup corresponding to a stochastic variational inequality [J].

Barbu, Viorel ;

Da Prato, Giuseppe .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2008, 33 (07) :1318-1338

[6] KOLMOGOROV EQUATION ASSOCIATED TO THE STOCHASTIC REFLECTION PROBLEM ON A SMOOTH CONVEX SET OF A HILBERT SPACE [J].

Barbu, Viorel ;

Da Prat, Giuseppe ;

Tubaro, Luciano .

ANNALS OF PROBABILITY, 2009, 37 (04) :1427-1458

[7] Multivalued Skorohod problem [J].

Cepa, E .

ANNALS OF PROBABILITY, 1998, 26 (02) :500-532

[8] Elliptic operators with unbounded drift coefficients and Neumann boundary condition [J].

Da Prato, G ;

Lunardi, A .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 198 (01) :35-52

[9]

Da Prato G., 1996, LONDON MATH SOC LECT, V229

[10]

DAPRATO G, 2004, AD CO MATH, pR9

← 1 2 →