ON STOCHASTIC GENERALIZED FUNCTIONS

被引：6

作者：

Catuogno, Pedro ^{[1
]}

Olivera, Christian ^{[1
]}

机构：

[1] Univ Estadual Campinas, Dept Matemat, BR-13081970 Campinas, SP, Brazil

来源：

INFINITE DIMENSIONAL ANALYSIS QUANTUM PROBABILITY AND RELATED TOPICS | 2011年 / 14卷 / 02期

基金：

巴西圣保罗研究基金会;

关键词：

White noise; Wick product; generalized functions; Colombeau algebras; parabolic equation; PARTIAL-DIFFERENTIAL-EQUATIONS;

D O I：

10.1142/S0219025711004407

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we introduce a new algebra of stochastic generalized functions. The regular Hida distributions in G* are embedded in this algebra via their chaos expansions. As an application, we prove the existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.

引用

页码：237 / 260

页数：24

共 30 条

[1]

Aase K., 2000, Finance Stoch, V4, P465, DOI [https://doi.org/10.1007/PL00013528, DOI 10.1007/PL00013528]

[2] A two-space dimensional semilinear heat equation perturbed by (Gaussian) white noise [J].

Albeverio, S ;

Haba, Z ;

Russo, F .

PROBABILITY THEORY AND RELATED FIELDS, 2001, 121 (03) :319-366

[3]

ALBEVERIO S, 1996, ISR MATH C P RAM GAR, V10, P1

[4]

Antosik P., 1973, Theory of distributions. The sequential approach

[5] Some regularity results for the stochastic pressure equation of Wick-type [J].

Benth, FE ;

Theting, TG .

STOCHASTIC ANALYSIS AND APPLICATIONS, 2002, 20 (06) :1191-1223

[6]

BENTH FE, 1996, STOCHASTICS, V58, P349

[7]

Biagioni H.A., 1990, Lecture Notes Mathematics, V1421

[8] Hermite expansions and products of tempered distributions [J].

Catuogno, Pedro ;

Molina, Sandra ;

Olivera, Christian .

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2007, 18 (04) :233-243

[9] GENERALIZED SOLUTION OF SOME PARABOLIC EQUATIONS WITH A RANDOM DRIFT [J].

CHOW, PL .

APPLIED MATHEMATICS AND OPTIMIZATION, 1989, 20 (01) :1-17

[10]

COLOMBEAU JF, 1985, N HOLLAND MATH STUDI, V113

← 1 2 3 →