Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

Fulbert KuessiAllognissode; Mamadou AbdoulDiop; KhalilEzzinbi; CarlosOgouyandjou

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Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

机译：由亚分数褐色运动，存在和渐近行为驱动的随机部分功能积分积分型方程

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摘要

This paper deals with the existence and uniqueness of mild solutions to stochastic partial functional integro-differential equations driven by a sub-fractional Brownian motion S Q H ? ( t ) {S_{Q}^{H}(t)} , with Hurst parameter H ∈ ( 1 2 , 1 ) {Hin(rac{1}{2},1)} . By the theory of resolvent operator developed by R. Grimmer (1982) to establish the existence of mild solutions, we give sufficient conditions ensuring the existence, uniqueness and the asymptotic behavior of the mild solutions. An example is provided to illustrate the theory.

机译：本文涉及由亚分数褐色运动驱动的随机部分功能积分微分方程的存在和唯一性 S. 问： H 还（ T. 的） {s_ {q} ^ {h}（t）} ，有赫斯特参数 H ∈ （ 1 2 那 1 的） {h in（ frac {1} {2}，1）} 。由R.Grimmer（1982）开发的解决方案操作员理论建立了轻度解决方案的存在，我们提供了充分的条件，确保了轻度解决方案的存在，独特性和渐近行为。提供一个例子来说明理论。

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来源
《Random operators and stochastic equations》 |2019年第2期|共16页
作者
Fulbert KuessiAllognissode; Mamadou AbdoulDiop; KhalilEzzinbi; CarlosOgouyandjou;
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作者单位

Institut de Mathématiques et de Sciences Physiques Université d’Abomey-Calavi (UAC) Porto Novo Benin;

Département de Mathématiques Université Gaston Berger de Saint-Louis UFR SAT 234 Saint-Louis Senegal;

Faculté des Sciences Semlalia Département de Mathématiques Université Cadi Ayyad F.B.P 2390 Marrakesh Morocco;

Institut de Mathématiques et de Sciences Physiques Université d’Abomey-Calavi (UAC) Porto Novo Benin;

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正文语种 eng
中图分类随机微分方程;
关键词
Existence and uniqueness; stochastic delay evolution equations; exponential decay in mean square; Resolvent operators; Wiener process; mild solutions; fractional Brownian motion; 60H15; 60G15;

机译：存在和唯一性;随机延迟演化方程;均方向的指数衰减;解析运营商;维纳过程;温和的解决方案;分数布朗运动;60H15;60G15;

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专利

1. Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior [J] . Fulbert KuessiAllognissode, Mamadou AbdoulDiop, KhalilEzzinbi, Random operators and stochastic equations . 2019,第2期

机译：由亚分数褐色运动，存在和渐近行为驱动的随机部分功能积分积分型方程
2. The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion [J] . Dehao Ruan, Jiaowan Luo Discrete dynamics in nature and society . 2018,第4期

机译：由标准布朗运动和分数布朗运动驱动的中立随机时滞偏微分方程的存在性，唯一性和可控制性
3. The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion [J] . Dehao Ruan, Jiaowan Luo Discrete dynamics in nature and society . 2018,第Pta1期

机译：标准布朗运动和分数布朗运动驱动中立随机延迟偏微分方程的存在，唯一性和可控性
4. Asymptotic analysis of a kernel estimator for stochastic differential equations driven by a mixed sub-fractional Brownian motion [C] . Abdelmalik Keddi, Fethi Madani, Amina Angelika Bouchentouf International Conference on Mathematics and Information Technology . 2020

机译：混合次分数布朗运动驱动的随机微分方程核估计的渐近分析
5. Stochastic functional differential equations driven by fractional Brownian motion and their generalizations [D] . Wilathgamuwa, Don Gayan Lasitha 2012

机译：分数布朗运动驱动的随机泛函微分方程及其推广
6. Exponential stability for neutral stochastic functional partial differential equations driven by Brownian motion and fractional Brownian motion [O] . Xinwen Zhang, Dehao Ruan -1

机译：由布朗运动和分数布朗运动驱动的中立型随机泛函偏微分方程的指数稳定性。
7. Asymptotic behavior of neutral stochastic partial functional integro-differential equations driven by a fractional Brownian motion [O] . Caraballo Garrido Tomás, Diop Mamadou Abdoul, Ndiaye Abdoul Aziz 2014

机译：由分数布朗运动驱动的中立型随机局部函数积分-微分方程的渐近行为

Stochastic partial functional integrodifferential equations driven by a sub-fractional Brownian motion, existence and asymptotic behavior

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