Research onstochastic partial differential equationswith some singularities

具有奇异性的随机偏微分方程研究

• 批准号: 21740067
• 负责人: XIE Bin
• 金额: $ 2.66万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Young Scientists (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21740067/
• 关键词: 確率論; 確率解析; 確率偏微分方程式; 爆発時刻; 確率微分方程式; Burgers方程式; ヤング図形; ヤング図モデル; 非平衡揺動極限; 爆発問題; Levyノイズ

In this project, I mainly did some researches on fundamental problems, explosion and ergodicity for stochastic partial differential equations with different singularities. In particular, I found that appropriate noise can delay the blow-up time of a nonlinear stochastic partial differential equation, deduced the well-knows Bismut-Elworthy formula for stochastic differential equations with Levy time noise. Moreover, as joint work, we deduced some new stochastic partial differential equations by the study of the fluctuation of two dimensional evolutionary Young diagrams.

在本项目中，我主要研究了具有不同奇异性的随机偏微分方程的基本问题、爆炸性和遍历性。特别地，我发现适当的噪声可以延迟一类非线性随机偏微分方程的爆破时间，推导出了著名的带Levy时间噪声的随机微分方程的Bismut-Elworthy公式。此外，作为合作工作，我们通过对二维演化杨氏图涨落的研究，导出了一些新的随机偏微分方程。

项目成果

Fluctuations in an evolutional model of two-dimensional Young diagrams

二维杨氏图演化模型中的涨落

• DOI: 10.1016/j.spa.2012.12.005
• 发表时间: 2013
• 期刊: Stoch. Proc. Appl.
• 作者: T. Funaki;M. Sasada;M. Sauer and B. Xie
• 通讯作者: M. Sauer and B. Xie

An SPDE with the distributions of Levy processes as its invariant measures

以 Levy 过程的分布作为其不变测度的 SPDE

• 发表时间: 2010
• 作者: M.Niu;B.Xie;B.Xie;舟木直久・謝賓;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;謝賓;B. Xie;謝賓;謝賓;B. Xie;謝賓;B. Xie;B. Xie
• 通讯作者: B. Xie

trong Feller property and irreducibility of stochastic differential equations driven by Levy noises

Levy噪声驱动的随机微分方程的强Feller性质和不可约性

• 发表时间: 2010
• 作者: M.Niu;B.Xie;B.Xie;舟木直久・謝賓;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;謝賓;B. Xie;謝賓;謝賓;B. Xie;謝賓;B. Xie
• 通讯作者: B. Xie

Regularity of a fractional partial differential equation driven by space-time white noise

• DOI: 10.1090/s0002-9939-09-10197-1
• 发表时间: 2010-04
• 作者: Min Niu;B. Xie

An SPDE with the laws of Levy processes as its invariant measures

以 Levy 过程定律作为不变测度的 SPDE

• 发表时间: 2010
• 作者: M.Niu;B.Xie;B.Xie;舟木直久・謝賓;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;B. Xie;B.Xie;B.Xie;B. Xie;B. Xie;謝賓;B. Xie;謝賓;謝賓
• 通讯作者: 謝賓