Potential Analysis最新文献_第4页

Total Variation Error Bounds for the Approximation of the Invariant Distribution of Parabolic Semilinear SPDEs Using the Standard Euler Scheme 使用标准欧拉方案逼近抛物线半线性 SPDE 的不变分布的总变差误差边界

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-19 DOI: 10.1007/s11118-024-10132-w

Charles-Edouard Bréhier

引用次数: 0

Exponential Contractivity and Propagation of Chaos for Langevin Dynamics of McKean-Vlasov Type with Lévy Noises 带列维噪声的麦金-弗拉索夫型兰万动力学的指数收缩性和混沌传播

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-15 DOI: 10.1007/s11118-024-10130-y

{"title":"Exponential Contractivity and Propagation of Chaos for Langevin Dynamics of McKean-Vlasov Type with Lévy Noises","authors":"","doi":"10.1007/s11118-024-10130-y","DOIUrl":"https://doi.org/10.1007/s11118-024-10130-y","url":null,"abstract":"<h3>Abstract</h3> By the probabilistic coupling approach which combines a new refined basic coupling with the synchronous coupling for Lévy processes, we obtain explicit exponential contraction rates in terms of the standard (L^1) -Wasserstein distance for the following Langevin dynamic ((X_t,Y_t)_{tge 0}) of McKean-Vlasov type on (mathbb R^{2d}) : $$begin{aligned} left{ begin{array}{l} dX_t=Y_t,dt, dY_t=left( b(X_t)+displaystyle int _{mathbb R^d}tilde{b}(X_t,z),mu ^X_t(dz)-{gamma }Y_tright) ,dt+dL_t,quad mu ^X_t=textrm{Law}(X_t), end{array} right. end{aligned}$$ where ({gamma }>0) , (b:mathbb R^drightarrow mathbb R^d) and (tilde{b}:mathbb R^{2d}rightarrow mathbb R^d) are two globally Lipschitz continuous functions, and ((L_t)_{tge 0}) is an (mathbb R^d) -valued pure jump Lévy process. The proof is also based on a novel distance function, which is designed according to the distance of the marginals associated with the constructed coupling process. Furthermore, by applying the coupling technique above with some modifications, we also provide the propagation of chaos uniformly in time for the corresponding mean-field interacting particle systems with Lévy noises in the standard (L^1) -Wasserstein distance as well as with explicit bounds.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"9 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140155562","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 $$L_{p}-$$ Theory for Integro-Differential Operators with Spatially Dependent Coefficients 关于具有空间依赖系数的积分微分算子的 $$L_{p}-$$ 理论

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-14 DOI: 10.1007/s11118-024-10131-x

Sutawas Janreung, Tatpon Siripraparat, Chukiat Saksurakan

引用次数: 0

Large and Moderate Deviations for Empirical Density Fields of Stochastic Seir Epidemics with Vertex-Dependent Transition Rates 顶点依赖转换率的随机 Seir 流行病经验密度场的大偏差和中偏差

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-09 DOI: 10.1007/s11118-024-10133-9

Xiaofeng Xue, Xueting Yin

引用次数: 0

Probabilistic Characterization of Weakly Harmonic Maps with Respect to Non-Local Dirichlet Forms 相对于非局部迪里希勒形式的弱谐波映射的概率特征

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-09 DOI: 10.1007/s11118-024-10129-5

Fumiya Okazaki

引用次数: 0

Stochastic Generalized Porous Media Equations Over $$sigma $$ -finite Measure Spaces with Non-continuous Diffusivity Function 具有非连续扩散函数的 $$sigma $$ - 无限测度空间上的随机广义多孔介质方程

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-03-04 DOI: 10.1007/s11118-024-10127-7

Michael Röckner, Weina Wu, Yingchao Xie

{"title":"Stochastic Generalized Porous Media Equations Over $$sigma $$ -finite Measure Spaces with Non-continuous Diffusivity Function","authors":"Michael Röckner, Weina Wu, Yingchao Xie","doi":"10.1007/s11118-024-10127-7","DOIUrl":"https://doi.org/10.1007/s11118-024-10127-7","url":null,"abstract":"In this paper, we prove that stochastic porous media equations over (sigma )-finite measure spaces ((E,mathcal {B},mu )), driven by time-dependent multiplicative noise, with the Laplacian replaced by a self-adjoint transient Dirichlet operator L and the diffusivity function given by a maximal monotone multi-valued function (Psi ) of polynomial growth, have a unique solution. This generalizes previous results in that we work on general measurable state spaces, allow non-continuous monotone functions (Psi ), for which, no further assumptions (as e.g. coercivity) are needed, but only that their multi-valued extensions are maximal monotone and of at most polynomial growth. Furthermore, an (L^p(mu ))-Itô formula in expectation is proved, which is not only crucial for the proof of our main result, but also of independent interest. The result in particular applies to fast diffusion stochastic porous media equations (in particular self-organized criticality models) and cases where E is a manifold or a fractal, and to non-local operators L, as e.g. (L=-f(-Delta )), where f is a Bernstein function.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"42 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140036020","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 Fourier Integral Formula for Logarithmic Energy 对数能量的傅立叶积分公式

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-09 DOI: 10.1007/s11118-024-10125-9

L. Frerick, J. Müller, T. Thomaser

引用次数: 0

Trace Operator on von Koch’s Snowflake 冯-科赫雪花上的微量运算符

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-09 DOI: 10.1007/s11118-024-10124-w

Krystian Kazaniecki, Michał Wojciechowski

{"title":"Trace Operator on von Koch’s Snowflake","authors":"Krystian Kazaniecki, Michał Wojciechowski","doi":"10.1007/s11118-024-10124-w","DOIUrl":"https://doi.org/10.1007/s11118-024-10124-w","url":null,"abstract":"We study properties of the boundary trace operator on the Sobolev space (W^1_1(Omega )). Using the density result by Koskela and Zhang (Arch. Ration. Mech. Anal. 222(1), 1-14 2016), we define a surjective operator (Tr: W^1_1(Omega _K)rightarrow X(Omega _K)), where (Omega _K) is von Koch’s snowflake and (X(Omega _K)) is a trace space with the quotient norm. Since (Omega _K) is a uniform domain whose boundary is Ahlfors-regular with an exponent strictly bigger than one, it was shown by L. Malý (2017) that there exists a right inverse to Tr, i.e. a linear operator (S: X(Omega _K) rightarrow W^1_1(Omega _K)) such that (Tr circ S= Id_{X(Omega _K)}). In this paper we provide a different, purely combinatorial proof based on geometrical structure of von Koch’s snowflake. Moreover we identify the isomorphism class of the trace space as (ell _1). As an additional consequence of our approach we obtain a simple proof of the Peetre’s theorem (Special Issue 2, 277-282 1979) about non-existence of the right inverse for domain (Omega ) with regular boundary, which explains Banach space geometry cause for this phenomenon.","PeriodicalId":49679,"journal":{"name":"Potential Analysis","volume":"92 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139762459","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 Universal Inequalities for Eigenvalues of a Clamped Plate Problem 夹板问题特征值的新通用不等式

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-02-08 DOI: 10.1007/s11118-024-10122-y

Yiling Jin, Shiyun Pu, Yuxia Wei, Yue He

引用次数: 0

Distribution-Path Dependent Nonlinear SPDEs with Application to Stochastic Transport Type Equations 分布路径依赖非线性 SPDEs 与随机传输型方程的应用

IF 1.1 3区数学

Potential Analysis Pub Date : 2024-01-31 DOI: 10.1007/s11118-023-10113-5

引用次数: 0