Non-linear expectations in spaces of Colombeau generalized functions

被引：1

作者：

Filinkov, Alexei ^{[1
]}

Elliott, Robert J. ^{[2
,3
]}

机构：

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA, Australia

[2] Univ Calgary, Haskayne Sch Business, Scurfield Hall,2500 Univ Dr NW, Calgary, AB T2N 1N4, Canada

[3] Univ South Australia, Sch Commerce, Ctr Appl Finance & Econ, Adelaide, SA 5001, Australia

来源：

STOCHASTIC ANALYSIS AND APPLICATIONS | 2019年 / 37卷 / 04期

基金：

澳大利亚研究理事会;

关键词：

Generalized solutions; Colombeau algebras; non-linear heat equation; G-expectation; backward stochastic differential equations; STOCHASTIC DIFFERENTIAL-EQUATIONS; BROWNIAN-MOTION; THEOREM; CALCULUS; DRIVEN;

D O I：

10.1080/07362994.2019.1585265

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of a non-linear expectation in spaces of Colombeau generalized functions and provide its characterization in terms of the upper expectation over a set of probability measures. We then study a fully non-linear backward stochastic differential equation in the Colombeau setting via its connection with the corresponding fully non-linear partial differential equation.

引用

页码：509 / 521

页数：13

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