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Stochastic quantization and ergodic theorem for density of diffusions

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Science China Mathematics 2012年第11期55卷 2285-2296页

作者： hu yaozhong Department of Mathematics University of Kansas Lawrence KS 66045 USA

For a given probability density function p（x） on R^d, we construct a （non-stationary） diffusion process xt, starting at any point x in R^d, such that 1/T ∫_o^T δ（xt-x）dt converges to p（x） almost surely. The rate of this convergence is also investigated. To find this rate, we mainly use the Clark-Ocone formula from Malliavin calculus and the Girsanov transformation technique.

关键词： Stochastic quantization diffusions Malliavan calculus ergodic theorem local time Clark-Oconeformula Girsanov formula Donsker delta functional heat kernel

SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS

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Acta Mathematica Scientia 2019年第3期39卷 874-914页

作者： yaozhong hu Department of Mathematical and Statistical Sciences University of Alberta

This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.

关键词： Gaussian random field Gaussian noise stochastic partial differential equation(stochastic heat equation) Feynman-Kac formula for the solution FeynmanKac formula for the moments of the solution chaos expansion hypercontractivity moment bounds Holder continuity joint Holder continuity asymptotic behaviour Trotter-Lie formula Skorohod integral

Solvability of Parabolic Anderson Equation with Fractional Gaussian Noise

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Communications in Mathematics and Statistics 2023年第3期11卷 563-582页

作者： Zhen-Qing Chen yaozhong hu Department of Mathematics University of WashingtonSeattleWA98195USA Department of Mathematical and Statistical Sciences University of Alberta at EdmontonEdmontonT6G 2G1Canada

This paper provides necessary as well as sufﬁcient conditions on the hurst parameters so that the continuous time parabolic Anderson model ∂u/∂t=1/2△+u˙W on[0,∞)×R^(d) with d≥1 has a unique randomﬁeld solution,where W(t,x)is a fractional Brownian sheet on[0,∞)×Rd and formally ˙W=∂d+1/∂t+∂x_(1)…∂x_(d)=W(t,x).When the noise W(t,x) is white in time,our condition is both necessary and sufﬁcient when the initial data u(0,x)is bounded between two positive *** the noise is fractional in time with hurst parameter H_(0)>1/2,our sufﬁcient condition,which improves the known results in the literature,is different from the necessary one.

关键词： Stochastic heat equation Fractional Brownian fields Wiener chaos expansion Random field solution Necessary condition sufficient condition Moment bounds

JOINT HOLDER CONTINUITY OF PARABOLIC ANDERSON MODEL

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Acta Mathematica Scientia 2019年第3期39卷 764-780页

作者： yaozhong hu Khoa Lê Department of Mathematical and Statistical Sciences University of Alberta Department of Mathematics South Kensington Campus Imperial College London

We obtain the H?lder continuity and joint H?lder continuity in space and time for the random field solution to the parabolic Anderson equation ■ in d-dimensional space, where ■ is a mean zero Gaussian noise with temporal covariance γ0 and spatial covariance given by a spectral density μ(ξ). We assume that ■ and ■ , where αi, i = 1, · · ·, d(or α) can take negative value.

关键词： Gaussian process stochastic heat equation parabolic Anderson model multiplicative noise chaos expansion hypercontractivity H?lder continuity joint Holder continuity

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

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Acta Mathematica Scientia 2019年第3期39卷 669-690页

作者： yaozhong hu Yanghui LIU Department of Mathematical and Statistical Sciences University of AlbertaEdmontonT6G 2G1Canada Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.

关键词： Stochastic heat equation general Gaussian noise L^(2) solution sufficient and necessary condition Wong-Zakai approximation pathwise solution Holder continuity Besov space

Tea polyphenol-gut microbiota interactions:hints on improving the metabolic syndrome in a multi-element and multi-target manner

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Food Science and human Wellness 2022年第1期11卷 11-21页

作者： hui Ma yaozhong hu Bowei Zhang Zeping Shao Eugeni Roura Shuo Wang a Tianjin Key Laboratory of Food Science and Health School of MedicineNankai UniversityTianjin 300071China Centre for Nutrition and Food Sciences Queensland Alliance for Agriculture and Food InnovationThe University of QueenslandBrisbaneQLD 4072Australia

The metabolic syndrome(MS)has become one of the main problems in public *** polyphenols(TPs),the main bioactive components of tea,has been claimed to have the potential to regulate metabolism and effectively prevent or mitigate the ***,many studies into the effects of TPs on MS have provided conflicting findings and the underlying mechanism has been *** predominant TPs in unfermentedand and fermented tea are catechins and oxidized polyphenols(theaflavins and thearubigins),both of which have low bioavailability and reach the colon where most gut microbes *** microbiota has been demonstrated to be tightly associated with host *** interactions between TPs and gut microbiota will lead to the alterations of gut microbiota composition and the production of metabolites including short chain fatty acids,bile acids,amino acids and TPs derived metabolites,accordingly exerting their biological effects both locally and *** review highlighted the contribution of metabolites and specific gut bacteria in the process of TPs intervention on the MS and further discuss how TPs impact the MS via gut microbiota from the viewpoint of gut organ/tissue axis.

关键词： Tea polyphenols Gut microbiota Metabolic syndrome Metabolites Gut organ/tissue axis

Nanobody-based food allergen surveillance:current status and prospects

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Food Quality and Safety 2024年第2期8卷 227-238页

作者： Yi Wang Sihao Wu Ang Li huan Lv Xuemeng Ji yaozhong hu Shuo Wang Tianjin Key Laboratory of Food Science and Health School of MedicineNankai UniversityTianjinChina

The incidence of food allergy has increased in recent decades,posing drastic risks to sensitive individuals,leading to mild to severe allergic *** is still no effective immune therapeutic strategy for food allergy that addresses accurate analytical methods to indicate the presence of allergens to prevent exposure of sensitive ***,the most commonly applied detection method is immunoassay developed with food allergen-specifc antibodies,especially the conventional formats of monoclonal antibodies(mAbs)and polyclonal antibodies(pAbs),which serve as dominant detection reagents for food allergen analysis,although with the disadvantages of being labor-intensive,costly,batch differences,and signifcant cross-reaction,***-derived nanobodies(Nbs)have attracted tremendous attention to explore their application in food hazard analysis because of robust characteristics like unique paratopes,high stability and affnity that strongly contribute to the benefcial ***,extensive analysis is needed to validate the potential use of Nbs as detection reagents and the advantages for food allergen *** reports have demonstrated the potential of Nbs for immunoassay development against food allergens,such as macadamia allergen Mac i 1,peanut allergens Ara h 1 and Ara h 3,lupin allergen Lup an 1,milk allergenβ-lactoglobulin,*** this review,we comprehensively summarize the structural and biochemical properties of Nbs that beneft the application of Nb-based immunoassay,as well as the representative detection strategies,to provide research data for newly developed Nb formats for food allergen analysis,and investigate the future establishment of Nb-based surveillance against major food allergens.

关键词： Food allergy food allergen nanobody immunoassay

Selection of specific nanobodies against peanut allergen through unbiased immunization strategy and the developed immuno-assay

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Food Science and human Wellness 2023年第3期12卷 745-754页

作者： yaozhong hu Chuan Zhang Jing Lin Yi Wang Sihao Wu Ying Sun Bowei Zhang huan Lv Xuemeng Ji Yang Lu Shuo Wang Tianjin Key Laboratory of Food Science and Health School of MedicineNankai UniversityTianjin 300071China College of Food Science and Engineering Tianjin University of Science and TechnologyTianjin 300457China

Peanut allergy is considered to be a major health issue with global *** date,no effective curative approach has been applied for the therapy of the anaphylaxis resulting from the peanut *** accurate and effective detection methods for the surveillance of allergens in food are still the primary strategies to avoid allergic *** this study,nanobodies(Nbs)derived from the Heavy-Chain only Antibodies(HCAbs)were selected against the general peanut protein extract through the unbiased strategy to facilitate the development of the sandwich ELISA for the detection and surveillance of peanut allergen *** target antigen of the selected Nb was identified as peanut allergen Ara h 3,and a cross-reaction was observed with the member of Gly 1 from the Ara h 3 *** applicability of the self-paired Nb P43 on the establishment of the immuno-assay was verified.A sandwich ELISA against peanut allergen was developed,which reached a linear range of 0.2-10.6μg/mL,and a limit of detection of 53.13 ng/mL.

关键词： Peanut allergen Ara h 3 Nanobody Sandwich ELISA Gly 1

Dirichlet过程及非参数Bayes模型

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中国科学：数学 2021年第11期51卷 1895-1932页

作者：张钧曦胡耀忠 Department of Mathematical and Statistical Sciences University of Alberta at EdmontonAlberta T6G 2G1Canada

自从Ferguson的里程碑式的工作以来,非参数Bayes模型在统计和机器学习等领域中有着广泛的应用,近年来得到了蓬勃的发展.它的一个重要的理论基础是一个特殊的随机概率测度族,即Dirichlet过程.本文介绍Dirichlet过程的构造、性质、推广以... 详细信息

自从Ferguson的里程碑式的工作以来,非参数Bayes模型在统计和机器学习等领域中有着广泛的应用,近年来得到了蓬勃的发展.它的一个重要的理论基础是一个特殊的随机概率测度族,即Dirichlet过程.本文介绍Dirichlet过程的构造、性质、推广以及它在非参数Bayes估计问题中的应用.另外,本文也提到双参数Poisson-Dirichlet过程、Beta过程和更一般的断棍(stick-breaking)过程以及相关性质.

关键词： Dirichlet过程断棍过程双参数Poisson-Dirichlet过程 Poisson过程中国餐馆模型印度自助餐模型非参数Bayes模型 U-统计量