L\'evy噪声驱动的非对称耗散随机系统的Poincar\'e-型不等式和分部积分公式

doi:10.12341/jssms12731

系统科学与数学 ›› 2016, Vol. 36 ›› Issue (2): 248-.DOI: 10.12341/jssms12731

L\'evy噪声驱动的非对称耗散随机系统的Poincar\'e-型不等式和分部积分公式

孙晓斌，谢颖超

江苏师范大学数学与统计学院, 徐州 221116

出版日期:2016-02-25 发布日期:2016-03-10

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孙晓斌，谢颖超. L\'evy噪声驱动的非对称耗散随机系统的Poincar\'e-型不等式和分部积分公式[J]. 系统科学与数学, 2016, 36(2): 248-.

SUN Xiaobin,XIE Yingchao. POINCAR\'E-TYPE INEQUALITY AND INTEGRATION BY PARTS FORMULA FOR NON-SYMMETRICAL DISSIPATIVE STOCHASTIC SYSTEMS DRIVEN BY L\'EVY NOISE[J]. Journal of Systems Science and Mathematical Sciences, 2016, 36(2): 248-.

POINCAR\'E-TYPE INEQUALITY AND INTEGRATION BY PARTS FORMULA FOR NON-SYMMETRICAL DISSIPATIVE STOCHASTIC SYSTEMS DRIVEN BY L\'EVY NOISE

SUN Xiaobin ,XIE Yingchao

School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116

Online:2016-02-25 Published:2016-03-10

研究了L\'evy噪声驱动的非对称耗散随机系统的mild解的存在唯一性以及不变测度的存在性, 随后得到了关于不变测度的Poincar\'e-型不等式和分部积分公式.

关键词： Poincar\'e-型不等式, 分部积分公式, L\'evy 噪声, 不变测度.

In this paper, we consider the non-symmetrical dissipative stochastic systems driven by L\'evy noise. We prove the existence and uniqueness of the mild solution and the existence of the invariant probability measure, and the Poincar\'e-type inequality and integration by parts formula with respect to the invariant probability measure.

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