Optimal control of stochastic system with Fractional Brownian Motion

In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because F...

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Auteurs principaux:	Chaofeng Zhao, Zhibo Zhai, Qinghui Du
Format:	article
Langue:	EN
Publié:	AIMS Press 2021
Sujets:	optimal harvesting control itô formula fractional brownian motion (fbm) maximum principle Biotechnology TP248.13-248.65 Mathematics QA1-939
Accès en ligne:	https://doaj.org/article/8c18524e61974e1399f5047c7e739c74
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id	oai:doaj.org-article:8c18524e61974e1399f5047c7e739c74
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spelling	oai:doaj.org-article:8c18524e61974e1399f5047c7e739c742021-11-09T02:32:07ZOptimal control of stochastic system with Fractional Brownian Motion10.3934/mbe.20212841551-0018https://doaj.org/article/8c18524e61974e1399f5047c7e739c742021-06-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021284?viewType=HTMLhttps://doaj.org/toc/1551-0018In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because FBM is neither a Markov pocess nor a semi-martingale. When the external environment impact on the system of FBM, the necessary and sufficient conditions for the optimization are offered through the stochastic maximum principle, Hamilton function and Itô formula in our work. To illustrate our study, we provide an example to demonstrate the obtained theoretical results, which is the expansion of certainty population system.Chaofeng ZhaoZhibo Zhai Qinghui Du AIMS Pressarticleoptimal harvesting controlitô formulafractional brownian motion (fbm)maximum principleBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 5625-5634 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	optimal harvesting control itô formula fractional brownian motion (fbm) maximum principle Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	optimal harvesting control itô formula fractional brownian motion (fbm) maximum principle Biotechnology TP248.13-248.65 Mathematics QA1-939 Chaofeng Zhao Zhibo Zhai Qinghui Du Optimal control of stochastic system with Fractional Brownian Motion
description	In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because FBM is neither a Markov pocess nor a semi-martingale. When the external environment impact on the system of FBM, the necessary and sufficient conditions for the optimization are offered through the stochastic maximum principle, Hamilton function and Itô formula in our work. To illustrate our study, we provide an example to demonstrate the obtained theoretical results, which is the expansion of certainty population system.
format	article
author	Chaofeng Zhao Zhibo Zhai Qinghui Du
author_facet	Chaofeng Zhao Zhibo Zhai Qinghui Du
author_sort	Chaofeng Zhao
title	Optimal control of stochastic system with Fractional Brownian Motion
title_short	Optimal control of stochastic system with Fractional Brownian Motion
title_full	Optimal control of stochastic system with Fractional Brownian Motion
title_fullStr	Optimal control of stochastic system with Fractional Brownian Motion
title_full_unstemmed	Optimal control of stochastic system with Fractional Brownian Motion
title_sort	optimal control of stochastic system with fractional brownian motion
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/8c18524e61974e1399f5047c7e739c74
work_keys_str_mv	AT chaofengzhao optimalcontrolofstochasticsystemwithfractionalbrownianmotion AT zhibozhai optimalcontrolofstochasticsystemwithfractionalbrownianmotion AT qinghuidu optimalcontrolofstochasticsystemwithfractionalbrownianmotion
_version_	1718441399926390784

Optimal control of stochastic system with Fractional Brownian Motion

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