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| 1 | L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms显示文摘In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with nonlocal branching mechanisms under a martingale change of measure. As an application of this decomposition,we obtain a necessary and sufficient condition(called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012),Kyprianou and Murillo-Salas(2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau(2018) for super Markov chains. | Zhen-Qing Chen Yan-Xia Ren Renming Song | 2019 | Science China Mathematics2019，62，8： | 3 |
| 2 | Uniform boundary Harnack principle for rotationally symmetric Lvy processes in general open sets显示文摘In this paper we prove the uniform boundary Harnack principle in general open sets for harmonic functions with respect to a large class of rotationally symmetric purely discontinuous Lvy processes. | KIM Panki SONG RenMing VONDRACEK Zoran | 2012 | Science China Mathematics2012，55，11： | 2 |
| 3 | Estimates on Green functions and Poisson kernels for symmetric stable processes显示文摘 | Zhen-Qing Chen Renming Song | 1998 | Mathematische Annalen1998，，3： | 1 |
| 4 | Suppression of explosion by polynomial noise for nonlinear differential systems显示文摘In this paper, we study the problem of the suppression of explosion by noise for nonlinear non-autonomous differential systems. For a deterministic non-autonomous differential system dx(t) =f(x(t), t)dt, which can explode at a finite time, we introduce polynomial noise and study the perturbed system dx(t) = f(x(t), t)dt + h(t)^(1/2)|x(t)|βAx(t)d B(t). We demonstrate that the polynomial noise can not only guarantee the existence and uniqueness of the global solution for the perturbed system, but can also make almost every path of the global solution grow at most with a certain general rate and even decay with a certain general rate(including super-exponential, exponential, and polynomial rates) under specific weak conditions. | Lichao FENG Shoumei LI Renming SONG Yemo LI | 2018 | Science China(Information Sciences)2018，61，7： | 1 |
| 5 | Global heat kernel estimate for relativistic stable processes in exterior open sets显示文摘 | Zhen-Qing Chen Panki Kim Renming Song | 2012 | Journal of Functional Analysis2012，，2： | 1 |
| 6 | Asymmetric non-Gaussian effects in a tumor growth model with immunization显示文摘 | Mengli Hao Jinqiao Duan Renming Song Wei Xu | 2014 | Applied Mathematical Modelling2014，，： | 1 |
| 7 | Levy Risk Model with Two-Sided Jumps and a Barrier Dividend Strategy 显示文摘 | Bo Lijun Song Renming Tang Dan | 2012 | Insurance: Mathematics and Economics2012，50，2： | 1 |
| 8 | Protective effect of Sheng-Nao-Kang decoction on focal cerebral ischemia-reperfusion injury in rats显示文摘 | Lin Chen Ye Zhao Tianlong Zhang Xuan Dang Renming Xie Zhenzhi Li Yang Li Yuli Li Wenna Zhao Hongru Song | 2014 | Journal of Ethnopharmacology2014，，： | 1 |
| 9 | Supercritical superprocesses: Proper normalization and non-degenerate strong limit显示文摘Suppose that X ={Xt, t≥0;Pμ} is a supercritical superprocess in a locally compact separable metric space E. Let φ0 be a positive eigenfunction corresponding to the first eigenvalue λ0 of the generator of the mean semigroup of X. Then Mt := e-λ0t〈φ0,Xt〉 is a positive martingale. Let M∞ be the limit of Mt. It is known(see Liu et al.(2009)) that M∞ is non-degenerate if and only if the L log L condition is satisfied. In this paper we are mainly interested in the case when the L log L condition is not satisfied. We prove that, under some conditions, there exist a positive function γt on [0,∞) and a non-degenerate random variable W such that for any finite nonzero Borel measure μ on E,lim/t→∞γt〈φ0,Xt〉=W, a.s.-Pμ.We also give the almost sure limit of γt〈f, Xt〉for a class of general test functions f. | Yan-Xia Ren Renming Song Rui Zhang | 2019 | Science China Mathematics2019，62，8： | 1 |
| 10 | Quasi-stationarity and quasi-ergodicity of general Markov processes显示文摘In this paper,we study the quasi-stationarity and quasi-ergodicity of general Markov processes.We show,among other things,that if X is a standard Markov process admitting a dual with respect to a finite measure m and if X admits a strictly positive continuous transition density p(t,x,y)(with respect to m)which is bounded in(x,y)for every t>0,then X has a unique quasi-stationary distribution and a unique quasi-ergodic distribution.We also present several classes of Markov processes satisfying the above conditions. | ZHANG JunFei LI ShouMei SONG RenMing | 2014 | Science China Mathematics2014，57，10： | 0 |
| 11 | Study on Pharmacological Effects of Peikun Pills显示文摘[Objectives]To explore the effects of Peikun Pill on blood pressure of healthy adult male rats.[Methods]The duodenum of anesthetized rats was given different doses of Peikun Pills,normal saline was used as a blank control group,and captopril was used as a positive western medicine control group.The systolic blood pressure,diastolic blood pressure,mean blood pressure and pulse pressure difference(systolic blood pressure-diastolic blood pressure),and heart rate were measured,myocardial tension time index was calculated,and statistical processing was performed.[Results]Peikun Pills have a significant pressure boosting effect,but have no effect on the myocardial tension time index.Captopril has the effects of lowering blood pressure,slowing down the heart rate and reducing the myocardial tension time index,and significantly increasing the pulse pressure difference.[Conclusions]Peikun Pills can increase blood pressure of rats.Peikun Pills are suitable for women with hypotension accompanied by anemia.However,patients with hypertension are prohibited to use. | Renming XIE Jinfeng CHEN Wangting SONG Lin YANG Xinyue ZHANG Lixia ZAN Shanshan ZHAO Mengqi YANG Min CHENG | 2020 | Medicinal Plant2020，11，6： | 0 |
| 12 | L log L criterion for a class of multitype superdiffusions with non-local branching mechanisms显示文摘In this paper, we provide a pathwise spine decomposition for multitype superdiffusions with non-local branching mechanisms under a martingale change of measure. As an application of this decomposition, we obtain a necessary and sufficient condition (called the L log L criterion) for the limit of the fundamental martingale to be non-degenerate. This result complements the related results obtained in Kyprianou et al.(2012), Kyprianou and Murillo-Salas (2013) and Liu et al.(2009) for superprocesses with purely local branching mechanisms and in Kyprianou and Palau (2018) for super Markov chains. | Zhen-Qing Chen Yan-Xia Ren Renming Song | 2019 | 中国科学:数学2019，49，8： | 0 |
| 13 | Sharp heat kernel estimates for spectral fractional Laplacian perturbed by gradients显示文摘Using Duhamel’s formula,we prove sharp two-sided estimates for the spectral fractional Laplacian’s heat kernel with time-dependent gradient perturbation in bounded C^1,1 domains.In addition,we obtain a gradient estimate as well as the Holder continuity of the heat kernel’s gradient. | Renming Song Longjie Xie Yingchao Xie | 2020 | Science China Mathematics2020，63，11： | 0 |
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