確率拡散方程式系

随机扩散方程组

• 批准号: 14J00047
• 负责人: TA TON V. (2015)
• 金额: $ 1.35万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for JSPS Fellows
• 财政年份: 2014
• 资助国家: 日本
• 起止时间: 2014-04-25 至 2016-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14J00047/
• 关键词: Stochastic PDEs; M-type 2 Banach spaces; Strict solutions; Mild solutions; Maximal regularity; Forest model; Evolution equations; Swarm behaviour model; Lotka-Volterra model

In this academic year, I studied the following two problems.1. Stochastic parabolic evolution equations of the form: dX+AXdt=[F_1(t)+F_2(X)]dt+G(t)dW(t) in Hilbert spaces and Banach spaces of M-type 2.First, I studied the linear case, i.e. F_2=0, in Hilbert spaces. Strong regularity of mild solutions to the equations has been shown. This result is published in Lithuanian Mathematical Journal(Volume 56 April 2016).Second, I handled the general case in Banach spaces of M-type 2. Strict solutions to that equations as well as their maximal regularity has been investigated. I submitted this study to an academic journal for possible publication.2. Non-autonomous stochastic linear evolution equations of the form: dX+A(t)Xdt=F(t)dt+G(t)dW(t) in Banach spaces of M-type 2. On the basis of the theory of deterministic linear evolution equations, I constructed strict solutions to the equations. This result is also submitted to an academic journal.

在这个学年，我研究了以下两个问题1。形式的随机抛物线进化方程：dx+axdt = [f_1（t）+f_2（x）] dt+g（t）dt+g（t）dw（t）在希尔伯特空间和m型的banach空间中。已经显示了对方程式的轻度解决方案的强界性。该结果发表在立陶宛数学期刊（2016年4月56日）。第二，我处理了M型2的Banach空间中的一般案例。已经研究了该方程式的严格解决方案以及其最大规律性。我将这项研究提交给可能出版的学术期刊2。形式的非自主随机线性演化方程：dx+a（t）xdt = f（t）dt+g（t）dt+g（t）dw（t）在m型2的Banach空间中。根据确定性线性进化方程的理论，我构建了对方程式的严格解决方案。该结果也已提交给学术期刊。

项目成果

White Noise and Stochastic Differential Equations

白噪声和随机微分方程

• 发表时间: 2014
• 作者: Ryo Ichijo;Hiroki Kobayashi;Saori Yoneda;Yui Iizuka;Shigeru Matsumura;Satsuki Kitano;Hitoshi Miyachi;Tetsuya Honda & Fumiko Toyoshima.;一條遼，小林大毅，米田早織，松村繁，本田哲也，豊島文子;一條 遼;一條 遼;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton
• 通讯作者: Ta Viet Ton

Stochastic partial differential equations in M-type 2 Banach spaces

• DOI: 10.1007/bf01048965
• 发表时间: 1995-02
• 期刊: Potential Analysis
• 影响因子: 1.1
• 作者: Z. Brzeźniak

Stochastic differential equations and some phenomena including noise

随机微分方程和包括噪声在内的一些现象

• 发表时间: 2015
• 作者: Ryo Ichijo;Hiroki Kobayashi;Saori Yoneda;Yui Iizuka;Shigeru Matsumura;Satsuki Kitano;Hitoshi Miyachi;Tetsuya Honda & Fumiko Toyoshima.;一條遼，小林大毅，米田早織，松村繁，本田哲也，豊島文子;一條 遼;一條 遼;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton
• 通讯作者: Ta Viet Ton

Existence and uniqueness of strict solutions of stochastic linear evolution equations in M-type 2 Banach spaces

M型2 Banach空间中随机线性演化方程严格解的存在唯一性

• 发表时间: 2015
• 作者: Ryo Ichijo;Hiroki Kobayashi;Saori Yoneda;Yui Iizuka;Shigeru Matsumura;Satsuki Kitano;Hitoshi Miyachi;Tetsuya Honda & Fumiko Toyoshima.;一條遼，小林大毅，米田早織，松村繁，本田哲也，豊島文子;一條 遼;一條 遼;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton
• 通讯作者: Ta Viet Ton

Maximal regularity for abstract stochastic linear evolution equations

抽象随机线性演化方程的最大正则性

• 发表时间: 2015
• 作者: Ryo Ichijo;Hiroki Kobayashi;Saori Yoneda;Yui Iizuka;Shigeru Matsumura;Satsuki Kitano;Hitoshi Miyachi;Tetsuya Honda & Fumiko Toyoshima.;一條遼，小林大毅，米田早織，松村繁，本田哲也，豊島文子;一條 遼;一條 遼;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton;Ta Viet Ton
• 通讯作者: Ta Viet Ton