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Necessary and sufficient conditions for path-independence of Girsanov transformation for infinite-dimensional stochastic evolution equations

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Frontiers of Mathematics in China 2014年第3期9卷 601-622页

作者： Miao WANG Jiang-lun wu Department of Mathematics Swansea University Swansea SA2 8PP UK School of Mathematics Northwest University Xi'an 710127 China

Based on a recent result on linking stochastic differential equations on R^d to （finite-dimensional） Burger-KPZ type nonlinear parabolic partial differential equations, we utilize Galerkin type finite-dimensional approximations to characterize the path-independence of the density process of Girsanov transformation for the infinite-dimensionl stochastic evolution equations. Our result provides a link of infinite-dimensional semi-linear stochastic differential equations to infinite-dimensional Burgers-KPZ type nonlinear parabolic partial differential equations. As an application, this characterization result is applied to stochastic heat equation in one space dimension over the unit interval.

关键词： Characterization theorem Burgers-KPZ type nonlinear equations in infinite dimensions infinite-dimensional semi-linear stochastic differential equations Galerkin approximation Girsanov transformation stochastic heat equation path-independence Frechet differentiation

Noise Effect on the 2D Stochastic Burgers Equation

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Acta Mathematica Sinica,English Series 2024年第9期40卷 2065-2090页

作者： Zhao DONG Jiang lun wu Guo Li ZHOU RCSDS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China Beijing Normal University-Hong Kong Baptist University United International College Zhuhai 519087P.R.China Guangdong Provincial Key Laboratory of Interdisciplinary Research and Application for Data Science(IRADS) UICZhuhai 519087P.R.China School of Statistics and Mathematics Chongqing University Key Laboratory of Nonlinear Analysis and Its Applications(Chongqing University) Ministry of EducationChongqing 400044P.R.China

By comprehensive utilizing of the geometry structure of 2D Burgers equation and the stochastic noise,we find the decay properties of the solution to the stochastic 2D Burgers equation with Dirichlet boundary ***,the e... 详细信息

关键词： 2D stochastic Burgers equation regularity

Ergodicity of 3D Stochastic Burgers Equation

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Acta Mathematica Sinica,English Series 2024年第2期40卷 498-510页

作者： Zhao DONG Jiang lun wu Guo Li ZHOU RCSDS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190P.R.China Department of Mathematics Computational FoundrySwansea UniversitySwansea SA18ENUK College of Mathematics and Statistics Chongqing UniversityChongqing 400044P.R.China

3D Burgers equation is an important model for *** is natural to expect the long-time behaviour for this hydrodynamics ***,there is no result about the long-time behaviour for this deterministic ***,if the system is perturbed by stochastic noise,we establish the existence and uniqueness of invariant measure for 3D stochastic Burgers equation.

关键词： 3D stochastic Burgers equations maximum principle ergodicity

Effects of N source and nitrification pretreatment on growth of Arthrospira platensis in human urine

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Journal of Zhejiang University-Science A(Applied Physics & Engineering) 2007年第11期8卷 1846-1852页

作者： FENG Dao-lun wu Zu-cheng WANG Da-hui Department of Environmental Science and Engineering Zhejiang University Hangzhou 310027 China

Culture ofArthrospiraplatensis （Spirulinaplatens） in human urine was investigated to get valuable biomass. NO3-N was the proper N source, in comparison with other N source, including urea, NH4-N and NO2-N. As a result, aerobic nitrification of human urine was performed, with above 93.6% nitrification percentage finally achieved with total-N （TN） load of 46.52 mg/（L.d）, in which Arthrospira platensis was successfully grown. The main compositions of the obtained biomass are close to those in Zarrouk medium. Thus, it is possible to culture Arthrospiraplatensis in nitrified human urine for food production within bioregenerative life support systems （BLSSs）.

关键词： Arthrospira platensis Human urine N source Nitrification Bioregenerative life support system (BLSS)

LEAST SQUARES ESTIMATOR FOR PATH-DEPENDENT MCKEAN-VLASOV SDES VIA DISCRETE-TIME OBSERVATIONS

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Acta Mathematica Scientia 2019年第3期39卷 691-716页

作者： Panpan REN Jiang-lun wu Department of Mathematics Computational Foundry Swansea University Bay Campus

In this article, we are interested in least squares estimator for a class of pathdependent McKean-Vlasov stochastic differential equations (SDEs). More precisely, we investigate the consistency and asymptotic distribution of the least squares estimator for the unknown parameters involved by establishing an appropriate contrast function. Comparing to the existing results in the literature, the innovations of this article lie in three aspects:(i) We adopt a tamed Euler-Maruyama algorithm to establish the contrast function under the monotone condition, under which the Euler-Maruyama scheme no longer works;(ii) We take the advantage of linear interpolation with respect to the discrete-time observations to approximate the functional solution;(iii) Our model is more applicable and practice as we are dealing with SDEs with irregular coefficients (for example, Holder continuous) and pathdistribution dependent.

关键词： McKean-Vlasov stochastic differential equation tamed Euler-Maruyama scheme weak monotonicity least squares estimator consistency asymptotic distribution

Residual dynamics of thiacloprid in medical herbs marjoram,thyme,and camomile in soil

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Journal of Environmental Sciences 2007年第2期19卷 205-209页

作者： YU Yun-long wu Jia-lun STAHLER Matthias PESTEMER Wilfried Department of Plant Protection College of Agriculture and Biotechnology Zhejiang University Hangzhou 310029 China Institute for Ecotoxicology and Ecochemistry in Plant Protection Federal Biological Research Centre for Agriculture and Forestry Koenigin-Luise-Strafle 19 D-14195 Berlin Germany

Thiacloprid is a new insecticide of the chloronicotinyl family. To assess its risk after application, residual characteristics of thiacloprid in marjoram, thyme, and camomile and in soil were studied under field conditions. The active ingredient was extracted from the plant material using a mixture of acetone-water. After filtration, the extract was concentrated to the aqueous phase, diluted with water, and portioned against ethyl acetate on a matrix solid phase dispersion column. Thiacloprid was extracted from soil using a mixture of methanol-water, filtered, and *** （clean up） with dichloromethane. The residues were quantified using HPLC-MS-MS. The methods were validated by recovery experiments. Thiacloprid residues in marjoram, thyme, and camomile and in soil persisted beyond 10, 14, 14, and 21 d but no residues were detected after 14, 21, 21, and 28 d, respectively. The data obtained in this study indicated that the biexponential model is more suitable than the first-order function to describe the decline of thiacloprid in fresh marjoram, fresh thyme, and dried camomile flowers with half-life （t1/2） of 1.1, 0.7, and 1.2 d, respectively. However, both the first-order function and biexponential model were found to be applicable for dissipation of thiacloprid in soil with almost the same t1/2 values of 3.5 and 3.6 d. The results indicated that thiacloprid dissipates rapidly and does not accumulate in the tested herbs and in soil.

关键词： thiacloprid marjoram (Majorana hortensis) thyme (Thymus vilgaris) camomile (Matricaria chamomilla) residue

Path independence of the additive functionals for stochastic differential equations driven by G-lévy processes

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Probability, Uncertainty and Quantitative Risk 2022年第2期7卷 101-118页

作者： Huijie Qiao Jiang-lun wu School of Mathematics Southeast UniversityNanjing 211189JiangsuChina Department of Mathematics University of Illinois at Urbana-ChampaignUrbanaIL 61801USA Department of Mathematics Computational FoundrySwansea UniversityBay CampusSwansea SA18ENUK

In this study,we are interested in stochastic differential equations driven by GLévy *** illustrate that a certain class of additive functionals of the equations of interest exhibits the path-independent property,gen... 详细信息

关键词： The path independence Additive functionals G-Lévy processes Stochastic differential equations driven by G-Lévy processes

A new method of pseudo absence data generation in landslide susceptibility mapping with a case study of Shenzhen

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Science China(Technological Sciences) 2010年第S1期53卷 75-84页

作者： XIAO ChenChao TIAN Yuan SHI WenZhong GUO QingHua wu lun Institute of Remote Sensing and Geographic Information System Peking UniversityBeijing 100871China University of Salzburg Z_GISCenter for GeoinformaticsSchillerstraβe 305020 SalzburgAustria Department of Land Surveying and Geo-Informatics Hong Kong Polytechnic UniversityHong KongChina School of Engineering University of California MercedMerced 95343USA

Landslide susceptibility mapping is a typical two-class classification problem where generating pseudo absence (non-slide) data plays an important *** this paper,a new method,target space exteriorization sampling method (TSES),is presented to generate pseudo absence data based on presence data directly in feature *** exteriorizes a presence sample to become a pseudo absence one by replacing the value of one of its features with a new one outside the value range of this feature of all presence *** method is compared with two existing methods,buffer controlled sampling (BCS) and iteratively refined sampling (IRS),in a study area of Shenzhen *** pseudo absence data generated by each of these three methods are organized into 20 subsets with increasing data sizes to study the effects of the proportion of pseudo absence data to presence *** landslide susceptibility maps of the study area are calculated with all these datasets by general additive model (GAM).It can be concluded that,through a 10-fold validation,TSES and IRS-based models have similar AUC values that are both greater than that of BCS,but TSES outperforms BCS and IRS in prediction *** results also have more reasonable spatial and histogram distributions than BCS and IRS,which can support categorization of an area into more susceptibility ranks,while IRS shows a tendency to separate the whole study area into two susceptibility *** can be also concluded that when using BCS,the pseudo absence data proportion to the presence data would be about 50% to get a considerable result,while for IRS or TSES the minimum proportion is 40%.

关键词： pseudo absence data landslide susceptibility mapping GIS GAM

AN AVERAGING PRINCIPLE FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS DRIVEN BY TIME-CHANGED LéVY NOISE

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Acta Mathematica Scientia 2022年第2期42卷 540-550页

作者： Guangjun SHEN Wentao XU Jiang-lun wu Department of Mathematics Anhui Normal UniversityWuhu 241000China Department of Mathematics Computational Foundry Swansea UniversitySwanseaSA18ENUK

In this paper,we aim to derive an averaging principle for stochastic differential equations driven by time-changed Lévy noise with variable *** certain assumptions,we show that the solutions of stochastic differential equations with time-changed Lévy noise can be approximated by solutions of the associated averaged stochastic differential equations in mean square convergence and in convergence in probability,*** convergence order is also estimated in terms of noise ***,an example with numerical simulation is given to illustrate the theoretical result.

关键词： Averaging principle stochastic differential equation time-changed Levy noise variable delays