Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation

In this paper, we consider a special nonlinear expectation problem on the special parameter space and give a necessary and sufficient condition for the existence of the solution. Meanwhile, we generalize the necessary and sufficient condition to the two-dimensional moment problem. Moreover, we use t...

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Main Authors:	Lei Gao, Dong Han
Format:	Article
Language:	English
Published:	MDPI AG 2019-01-01
Series:	Mathematics
Subjects:	moment problem maximum entropy nonlinear expectation existence and uniqueness
Online Access:	http://www.mdpi.com/2227-7390/7/1/45

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spelling	doaj-8ebab205acb3465a84a38bc2bd90c4d42020-11-24T23:24:42ZengMDPI AGMathematics2227-73902019-01-01714510.3390/math7010045math7010045Methods of Moment and Maximum Entropy for Solving Nonlinear ExpectationLei Gao0Dong Han1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, ChinaDepartment of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, ChinaIn this paper, we consider a special nonlinear expectation problem on the special parameter space and give a necessary and sufficient condition for the existence of the solution. Meanwhile, we generalize the necessary and sufficient condition to the two-dimensional moment problem. Moreover, we use the maximum entropy method to carry out a kind of concrete solution and analyze the convergence for the maximum entropy solution. Numerical experiments are presented to compute the maximum entropy density functions.http://www.mdpi.com/2227-7390/7/1/45moment problemmaximum entropynonlinear expectationexistence and uniqueness
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lei Gao Dong Han
spellingShingle	Lei Gao Dong Han Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation Mathematics moment problem maximum entropy nonlinear expectation existence and uniqueness
author_facet	Lei Gao Dong Han
author_sort	Lei Gao
title	Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation
title_short	Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation
title_full	Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation
title_fullStr	Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation
title_full_unstemmed	Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation
title_sort	methods of moment and maximum entropy for solving nonlinear expectation
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-01-01
description	In this paper, we consider a special nonlinear expectation problem on the special parameter space and give a necessary and sufficient condition for the existence of the solution. Meanwhile, we generalize the necessary and sufficient condition to the two-dimensional moment problem. Moreover, we use the maximum entropy method to carry out a kind of concrete solution and analyze the convergence for the maximum entropy solution. Numerical experiments are presented to compute the maximum entropy density functions.
topic	moment problem maximum entropy nonlinear expectation existence and uniqueness
url	http://www.mdpi.com/2227-7390/7/1/45
work_keys_str_mv	AT leigao methodsofmomentandmaximumentropyforsolvingnonlinearexpectation AT donghan methodsofmomentandmaximumentropyforsolvingnonlinearexpectation
_version_	1725559378657935360

Methods of Moment and Maximum Entropy for Solving Nonlinear Expectation

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