Convolution Equation: Solution and Probabilistic Representation

被引：3

作者：

Da Silva, Jose L. ^{[1
]}

Erraoui, Mohamed ^{[2
]}

Ouerdiane, Habib ^{[3
]}

机构：

[1] Univ Madeira, Math & Engn Dept, P-9000390 Funchal, Madeira, Portugal

[2] Univ Cadi Ayyad, Dept Math, Marrakech 2390, BP, Morocco

[3] Univ Tunis El Manar, Dept Math, Tunis 1060, Tunisia

来源：

QUANTUM PROBABILITY AND INFINITE DIMENSIONAL ANALYSIS | 2010年 / 25卷

关键词：

Generalized functions; convolution; adjoint operator; Cauchy problem; stochastic integrals in Hilbert space; OPERATORS;

D O I：

10.1142/9789814295437_0016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a Cauchy problem associated to Delta(K)*, the adjoint of Delta K which is related to the Gross Laplacian for certain choice of the operator K. We show that the solution is a well defined generalized function in an appropriate space. Finally, using infinite dimensional stochastic calculus we give a probabilistic representation of the solution in terms of K-Wiener process W.

引用

页码：230 / +

页数：4

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