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Acta Mathematica Sinica,English Series 2025年

作者： zhenlong chen Peng Xu School of Statistics and Mathematics Zhejiang Gongshang University

Let X={X（t）, t∈RN}be a centered space-time anisotropic Gaussian random field with values in Rd. Under some general conditions, the existence, joint continuity and H¨older conditions of higher-order derivative of local times of X are studied. Moreover, we obtain the uniform Hausdorff dimension of the inverse images of X. The existing results of Gaussian random fields are extended to space-time anisotropic Gaussian random fields with approximate independent components.

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The Optimal Dividend Barrier in the Perturbed Compound Poisson Risk Model with Randomized Observation Time

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Journal of Systems Science & Complexity 2015年第2期28卷 451-470页

作者： LIU Xiao chen zhenlong MING Ruixing School of Statistics and Mathematics Zhejiang Gongshang University

This paper considers the dividend problems in the perturbed compound Poisson risk *** that dividends can only be paid at the observation time when the surplus exceeds the barrier level and the excess is paid as *** this paper,integro-differential equations for the expected discounted dividends until ruin and the Laplace transform of ruin time are firstly *** the claim is exponentially distributed,explicit expressions for the expected discounted dividends until ruin and the Laplace transform of ruin time are also ***,the optimal dividend barrier which maximizes the expected discounted dividends until ruin is given.

关键词： Barrier strategy dividend perturbed compound Poisson risk model ruin.

Smoothness of local times and self-intersection local times of Gaussian random fields

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Frontiers of Mathematics in China 2015年第4期10卷 777-805页

作者： zhenlong chen DongshengWU Yimin XIAO School of Statistics and Mathematics Zhejiang Gongshang University Hangzhou 310018 China Department of Mathematical Sciences University of Alabama in HuntsvilleHuntsville AL 35899 USA Department of Statistics and Probability Michigan State UniversityEast Lansing MI 48824 USA

This paper is concerned with the smoothness （in the sense of Meyer- Watanabe） of the local times of Gaussian random fields. Sufficient and necessary conditions for the existence and smoothness of the local times, collision local times, and self-intersection local times are established for a large class of Gaussian random fields, including fractional Brownian motions, fractional Brownian sheets and solutions of stochastic heat equations driven by space-time Gaussian noise.

关键词： Anisotropic Gaussian field local time collision local time,intersection local time self-intersection local time chaos expansion

On intersections of independent anisotropic Gaussian random fields

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Science China Mathematics 2012年第11期55卷 2217-2232页

作者： chen zhenlong XIAO YiMin School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China Department of Statistics and Probability Michigan State UniversityEast Lansing:MI 48824USA

Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.

关键词： intersection anisotropic Gaussian fields hitting probability Hausdorff dimension stochastic heatequation fractional Brownian sheet

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

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Acta Mathematica Scientia 2022年第2期42卷 653-670页

作者： Jun WANG zhenlong chen School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou 310018China School of Mathematics and Finance Chuzhou UniversityChuzhou 239000China

Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are *** an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

关键词： Hitting probability multiple intersection anisotropic random field capacity Hausdorff dimension stochastic fractional heat equations

Correlations for the ignition delay times of hydrogen/air mixtures

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Chinese Science Bulletin 2011年第2期56卷 215-221页

作者： ZHAO zhenlong chen Zheng chen ShiYi State Key Laboratory for Turbulence and Complex Systems College of Engineering Peking University Beijing 100871 China

Correlations for the ignition delay times of hydrogen/air mixtures were developed using the method of High Dimensional Model Representation (HDMR).The hydrogen/air ignition delay times for initial conditions over a wide range of temperatures from 800 to 1600 K,pressures from 0.1 to 100 atm,and equivalence ratios from 0.2 to 10 were first calculated utilizing the full chemical *** were then developed based on these ignition delay *** forms of correlations were constructed:the first one is an overall general model covering the whole range of the initial conditions;while the second one is a piecewise correlation model valid for initial conditions within different *** performance of these correlations was studied through comparison with results from the full chemical mechanism as well as experimental *** was shown that these correlations work well over the whole range of initial conditions and that the accuracy can be significantly improved by using different piecewise correlations for different ***,piecewise correlations can be used as an effective replacement for the full mechanism when the prediction of chemical time scale is needed in certain combustion modeling.

关键词：点火延迟时间空气混合物氢化学机制开发利用模型表示温度范围一般模型

Some Polar Sets for the Generalized Brownian Sheet

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Wuhan University Journal of Natural Sciences 2008年第2期13卷 137-140页

作者： LI Huiqiong LIU Luqin chen zhenlong College of Statistics and Mathematics Zhejiang GongshangUniversity Hangzhou 310018 Zhejiang China School of Mathematics and Statistics Wuhan UniversityWuhan 430072 Hubei China

Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.

关键词： generalized Brownian sheet polar set single point multiple points

MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

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Acta Mathematica Scientia 2024年第1期44卷 275-294页

作者：陈振龙苑伟杰 School of Statistics and Mathematics Zhejiang Gongshang UniversityHangzhou310018China

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain ***,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are *** results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

关键词： anisotropic Gaussian field multiple intersections Hausdorff measure capacity

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

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Acta Mathematica Scientia 2023年第3期43卷 1403-1414页

作者：裴雯熠闫理坦陈振龙 School of Statistics and Mathematics Zhejiang Gongshang UniversityZhejiang310018China Collaborative Innovation Center of Statistical Data Engineering Technology&ApplicationZhejiang Gongshang UniversityZhejiang310018China Department of Statistics Donghua UniversityShanghai201620China

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H... 详细信息

关键词： stochastic differential equations Harnack type inequalities fractional Brownian motion Markovian switching

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延川南深部煤层气田地质单元划分及开发对策

煤田地质与勘探 2021年第2期49卷 13-20页

作者：陈贞龙中国石油化工股份有限公司华东油气分公司江苏南京210011

我国深部煤层气资源潜力大,占总资源量的62.8%,但实现有效开发面临强非均质性、高地应力、工艺配套难、产能低等诸多挑战。以延川南深部煤层气田为例,依据“沉积控煤、构造控藏、水动力控气、地应力控渗、物性控产”五要素,将关键参数... 详细信息

我国深部煤层气资源潜力大,占总资源量的62.8%,但实现有效开发面临强非均质性、高地应力、工艺配套难、产能低等诸多挑战。以延川南深部煤层气田为例,依据“沉积控煤、构造控藏、水动力控气、地应力控渗、物性控产”五要素,将关键参数进行叠加,精细划分气田开发地质单元,厘清各开发地质单元关键地质属性、开发制约条件,并制定了差异化的开发对策;形成针对层内阻塞、近井地带结垢、深部煤层难改造、高液量难降压等不同低效主因的治理对策和适用于深部煤层气复杂地质条件下“疏导解堵、扰动增透、有效支撑、提液降压”的增效技术系列。在此基础上,提出了一整套基于“多要素耦合气藏控制单元”的地质工程一体化增效思路和工艺技术:以提高资源动用程度为核心,针对高产区煤粉阻碍渗流通道而造成的气井递减,采取“氮气扰动”形成压力波扰动而解决层内疏通,21口井见气效率90%,单井日增产气量400 m^(3);深部煤层矿化度高易在近井筒地带结垢是导致低产的重要因素,通过实施可控冲击波破裂增透解除堵塞,单井日增产气量达850 m^(3);以实现高应力区资源有效动用为目标,通过“长距离有效支撑、大规模体积改造”以达到深部煤储层有效改造,实现难动储量效益开发,实施16口井全部见效,单井日增产气量1500 m^(3),产气水平提升5~6倍;同时在高产液低效井中持续挖潜,采取提液降压效果初步显现。一体化增效关键技术体系的研发成功,为国内深部煤层气效益开发起到了带动和示范作用。

关键词：深部煤层气延川南地质工程一体化多要素耦合效益开发低产增效