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Berry–Esseen Bounds and Cramér-Type Moderate Deviations for the Sample Mean and the MLE of the Growth Rate for a Jump-Type CIR Process 跳跃型CIR过程增长率的样本均值和最大似然值的Berry-Esseen边界和cram<s:1> - type中等偏差
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3231-5
Fuqing Gao, Zhi Qu
{"title":"Berry–Esseen Bounds and Cramér-Type Moderate Deviations for the Sample Mean and the MLE of the Growth Rate for a Jump-Type CIR Process","authors":"Fuqing Gao,&nbsp;Zhi Qu","doi":"10.1007/s10114-025-3231-5","DOIUrl":"10.1007/s10114-025-3231-5","url":null,"abstract":"<div><p>We study Berry–Esseen bounds and Cramér-type moderate deviations of a jump-type Cox–Ingersoll–Ross (CIR) process driven by a standard Wiener process and a subordinator. In the subcritical case, we obtain the best Berry–Esseen bound of the sample mean and the MLE of the growth rate if the Lévy measure of the subordinator has finite third order moment. Under the Cramér condition, we establish the Cramér-type moderate deviations of the MLE of the growth rate. We first derive a Berry–Esseen bound, a deviation inequality and the Cramér-type moderate deviations for the sample mean of the CIR process by analyzing the asymptotic behaviors of the characteristic function and the moment generating function of the sample mean. Then we analyze a type of additive functional of the jump-type CIR process and use a transformation to study the Berry–Esseen bound and the Cramér-type moderate deviations for the MLE of the growth rate.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1508 - 1530"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New Product Formulas for Classical Gauss Sums 经典高斯和的新乘积公式
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3543-5
Wenpeng Zhang, Li Wang
{"title":"New Product Formulas for Classical Gauss Sums","authors":"Wenpeng Zhang,&nbsp;Li Wang","doi":"10.1007/s10114-025-3543-5","DOIUrl":"10.1007/s10114-025-3543-5","url":null,"abstract":"<div><p>The main purpose of this article is using the elementary techniques and the properties of the character sums to study the computational problem of one kind products of Gauss sums, and give an interesting triplication formula for them.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1580 - 1590"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Semirings with Invariant Basis Numbers 基数不变的半环
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3155-0
Qianyu Shu, Xueping Wang
{"title":"The Semirings with Invariant Basis Numbers","authors":"Qianyu Shu,&nbsp;Xueping Wang","doi":"10.1007/s10114-025-3155-0","DOIUrl":"10.1007/s10114-025-3155-0","url":null,"abstract":"<div><p>In this paper, the semirings with invariant basis numbers are investigated. First, we give some properties of a semiring which has an invariant basis number, and then give some necessary and sufficient conditions that the direct sum of two semirings has an invariant basis number. As an application, we prove that division semirings, quasilocal semirings and stably finite semirings have invariant basis numbers, respectively.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1565 - 1579"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143418","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On a Class of Finsler Metrics of Douglas Type 一类Douglas型Finsler度量
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-06-15 DOI: 10.1007/s10114-025-3309-0
Huaifu Liu, Xiaohuan Mo
{"title":"On a Class of Finsler Metrics of Douglas Type","authors":"Huaifu Liu,&nbsp;Xiaohuan Mo","doi":"10.1007/s10114-025-3309-0","DOIUrl":"10.1007/s10114-025-3309-0","url":null,"abstract":"<div><p>In this paper, we study a class of Finsler metrics of cohomogeneity two on ℝ × ℝ<sup><i>n</i></sup>. They are called <i>weakly orthogonally invariant Finsler metrics</i>. These metrics not only contain spherically symmetric Finsler metrics and Marcal–Shen’s warped product metrics but also partly contain another “warping” introduced by Chen–Shen–Zhao. We obtain differential equations that characterize weakly orthogonally invariant Finsler metrics with vanishing Douglas curvature, and therefore we provide a unifying frame work for Douglas equations due to Liu–Mo, Mo–Solórzano–Tenenblat and Solórzano. As an application, we obtain a lot of <i>new</i> examples of weakly orthogonally invariant Douglas metrics.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 6","pages":"1491 - 1507"},"PeriodicalIF":0.9,"publicationDate":"2025-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145143413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Some Discrete Bonnesen-style Isoperimetric Inequalities 关于一些离散bonnesen型等周不等式
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3281-8
Chunna Zeng, Xu Dong
{"title":"On Some Discrete Bonnesen-style Isoperimetric Inequalities","authors":"Chunna Zeng,&nbsp;Xu Dong","doi":"10.1007/s10114-025-3281-8","DOIUrl":"10.1007/s10114-025-3281-8","url":null,"abstract":"<div><p>This article deals with the sharp discrete isoperimetric inequalities in analysis and geometry for planar convex polygons. First, the analytic isoperimetric inequalities based on the Schur convex function are established. In the wake of the analytic isoperimetric inequalities, Bonnesen-style isoperimetric inequalities and inverse Bonnesen-style inequalities for the planar convex polygons are obtained.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1447 - 1461"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Special Value Distribution of Two Classes of Small Multiplicative Functions 两类小乘法函数的特殊值分布
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3125-6
Haihong Fan, Wenguang Zhai
{"title":"On the Special Value Distribution of Two Classes of Small Multiplicative Functions","authors":"Haihong Fan,&nbsp;Wenguang Zhai","doi":"10.1007/s10114-025-3125-6","DOIUrl":"10.1007/s10114-025-3125-6","url":null,"abstract":"<div><p>For any real number <i>x</i>, [<i>x</i>] denotes the integer part of <i>x</i>. <span>(cal{F})</span><sub>1</sub>, <span>(cal{F})</span><sub>2</sub> denote two multiplicative function classes which are small in numerical sense. In this paper, we study the summation <span>(sumnolimits_{{nleq x}}f([x/n]))</span> for <i>f</i> ∈ <span>(cal{F})</span><sub>1</sub>. As specific cases, we take <i>d</i><sup>(<i>e</i>)</sup>(<i>n</i>), <i>β</i>(<i>n</i>), <i>a</i>(<i>n</i>), <i>μ</i><sub>2</sub>(<i>n</i>) denoting the number of exponential divisors of <i>n</i>, the number of square-full divisors of <i>n</i>, the number of non-isomorphic Abelian groups of order <i>n</i>, and the characteristic function of the square-free integers, respectively. In the case of <i>μ</i><sub>2</sub>(<i>n</i>), we improved the result of Liu, Wu and Yang. The sums shaped like <span>(sumnolimits_{{nleq x}}f([x/n]+f([x/n])))</span> for <i>f</i> ∈ <span>(cal{F})</span><sub>2</sub> are also researched.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1407 - 1417"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Well-Posedness for McKean–Vlasov SDEs Driven by Multiplicative Stable Noises 乘性稳定噪声驱动下McKean-Vlasov SDEs的适定性
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-4030-8
Changsong Deng, Xing Huang
{"title":"Well-Posedness for McKean–Vlasov SDEs Driven by Multiplicative Stable Noises","authors":"Changsong Deng,&nbsp;Xing Huang","doi":"10.1007/s10114-025-4030-8","DOIUrl":"10.1007/s10114-025-4030-8","url":null,"abstract":"<div><p>We establish the well-posedness for a class of McKean–Vlasov SDEs driven by symmetric <i>α</i>-stable Lévy processes (<span>({1 over 2} &lt;alpha leq 1)</span>), where the drift coefficient is Hölder continuous in space variable, while the noise coefficient is Lipscitz continuous in space variable, and both of them satisfy the Lipschitz condition in distribution variable with respect to Wasserstein distance. If the drift coefficient does not depend on distribution variable, our methodology developed in this paper applies to the case <i>α</i> ∈ (0, 1]. The main tool relies on heat kernel estimates for (distribution independent) stable SDEs and Banach’s fixed point theorem.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1269 - 1278"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nearest Point Maps onto Uniformly Convex Sets 最近点映射到一致凸集上
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3598-3
Qingjin Cheng, Cuiling Wang, Jianjian Wang
{"title":"Nearest Point Maps onto Uniformly Convex Sets","authors":"Qingjin Cheng,&nbsp;Cuiling Wang,&nbsp;Jianjian Wang","doi":"10.1007/s10114-025-3598-3","DOIUrl":"10.1007/s10114-025-3598-3","url":null,"abstract":"<div><p>Let <i>K</i> be a (bounded) closed uniformly convex subset of a Banach space <i>X</i>. We show that\u0000</p><ol>\u0000 <li>\u0000 <span>(i)</span>\u0000 \u0000 <p>the nearest point map is well-defined and always continuous from <i>X</i> onto <i>K</i>,</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(ii)</span>\u0000 \u0000 <p>there is a reflexive space <i>Y</i> with a uniform rotund in every direction norm such that <i>Y</i> contains <i>K</i> as a subset and the nearest point map <i>P</i><sub><i>K</i></sub>: <i>Y</i> → <i>K</i> is uniformly continuous from any bounded set containing <i>K</i> onto <i>K</i>.</p>\u0000 \u0000 </li>\u0000 </ol></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1315 - 1327"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Holomorphic Koszul–Brylinski Homologies of Poisson Blow-ups 泊松膨胀的全纯Koszul-Brylinski同调
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-2365-9
Xiaojun Chen, Youming Chen, Song Yang, Xiangdong Yang
{"title":"Holomorphic Koszul–Brylinski Homologies of Poisson Blow-ups","authors":"Xiaojun Chen,&nbsp;Youming Chen,&nbsp;Song Yang,&nbsp;Xiangdong Yang","doi":"10.1007/s10114-025-2365-9","DOIUrl":"10.1007/s10114-025-2365-9","url":null,"abstract":"<div><p>We derive a blow-up formula for holomorphic Koszul–Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the <i>E</i><sub>1</sub>-degeneracy of the Dolbeault–Koszul–Brylinski spectral sequence under Poisson blow-ups, and compute the holomorphic Koszul–Brylinski homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic Poisson structures.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1462 - 1490"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Class of p-Laplacian Equations on Lattice Graphs 格图上的一类p-拉普拉斯方程
IF 0.9 3区 数学
Acta Mathematica Sinica-English Series Pub Date : 2025-05-15 DOI: 10.1007/s10114-025-3304-5
Lidan Wang
{"title":"A Class of p-Laplacian Equations on Lattice Graphs","authors":"Lidan Wang","doi":"10.1007/s10114-025-3304-5","DOIUrl":"10.1007/s10114-025-3304-5","url":null,"abstract":"<div><p>In this paper, we study the <i>p</i>-Laplacian equation of the form </p><div><div><span>$$-Delta_{p}u+h(x)vert u vert^{p-2}u=(R_{alpha}* vert u vert^{q})vert u vert^{q-2}u+vert u vert ^{2q-2}u$$</span></div></div><p> on lattice graphs ℤ<sup><i>N</i></sup>, where <i>N</i> ∈ ℕ*, <i>α</i> ∈ (0, <i>N</i>), <span>(2 leq p &lt; {2Nq over N+alpha}&lt;+infty)</span> and <i>R</i><sub><i>α</i></sub> represents the Green’s function of the discrete fractional Laplacian, which has no singularity at the origin but behaves as the Riesz potential at infinity. Under suitable assumptions on the potential <i>h</i>(<i>x</i>), we prove the existence of ground state solutions to the equation above by two different methods.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 5","pages":"1418 - 1430"},"PeriodicalIF":0.9,"publicationDate":"2025-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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