Analysis and Applications最新文献_第9页

Learning theory of minimum error entropy under weak moment conditions 弱矩条件下最小误差熵学习理论

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-03-06 DOI: 10.1142/S0219530521500044

Shouyou Huang, Yunlong Feng, Qiang Wu

引用次数: 9

Robust wavelet-based estimation for varying coefficient dynamic models under long-dependent structures 长相关结构下变系数动态模型的鲁棒小波估计

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-03-06 DOI: 10.1142/S0219530521500032

Xingcai Zhou, Shaogao Lv

引用次数: 0

Deep relu neural networks overcome the curse of dimensionality for partial integrodifferential equations 深度relu神经网络克服偏积分微分方程的维数诅咒

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-02-23 DOI: 10.1142/s0219530522500129

Lukas Gonon, C. Schwab

{"title":"Deep relu neural networks overcome the curse of dimensionality for partial integrodifferential equations","authors":"Lukas Gonon, C. Schwab","doi":"10.1142/s0219530522500129","DOIUrl":"https://doi.org/10.1142/s0219530522500129","url":null,"abstract":"Deep neural networks (DNNs) with ReLU activation function are proved to be able to express viscosity solutions of linear partial integrodifferental equations (PIDEs) on state spaces of possibly high dimension $d$. Admissible PIDEs comprise Kolmogorov equations for high-dimensional diffusion, advection, and for pure jump L'{e}vy processes. We prove for such PIDEs arising from a class of jump-diffusions on $mathbb{R}^d$, that for any compact $Ksubset mathbb{R}^d$, there exist constants $C,{mathfrak{p}},{mathfrak{q}}>0$ such that for every $varepsilon in (0,1]$ and for every $din mathbb{N}$ the normalized (over $K$) DNN $L^2$-expression error of viscosity solutions of the PIDE is of size $varepsilon$ with DNN size bounded by $Cd^{mathfrak{p}}varepsilon^{-mathfrak{q}}$. In particular, the constant $C>0$ is independent of $din mathbb{N}$ and of $varepsilon in (0,1]$ and depends only on the coefficients in the PIDE and the measure used to quantify the error. This establishes that ReLU DNNs can break the curse of dimensionality (CoD for short) for viscosity solutions of linear, possibly degenerate PIDEs corresponding to Markovian jump-diffusion processes. As a consequence of the employed techniques we also obtain that expectations of a large class of path-dependent functionals of the underlying jump-diffusion processes can be expressed without the CoD.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41767821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 15

Sobolev meets Besov: Regularity for the Poisson equation with Dirichlet, Neumann and mixed boundary values Sobolev满足Besov：具有Dirichlet、Neumann和混合边值的Poisson方程的正则性

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-02-19 DOI: 10.1142/s0219530522500026

C. Schneider, Flóra Orsolya Szemenyei

引用次数: 1

Gabor frame characterisations of generalised modulation spaces 广义调制空间的Gabor帧特征

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-02-05 DOI: 10.1142/s0219530522500178

A. Debrouwere, B. Prangoski

引用次数: 2

On the Spherical Slice Transform 关于球片变换

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-01-17 DOI: 10.1142/s021953052150024x

B. Rubin

引用次数: 4

Modified proximal symmetric ADMMs for multi-block separable convex optimization with linear constraints 线性约束下多块可分凸优化的改进近端对称admm

IF 2.2 2区数学

Analysis and Applications Pub Date : 2021-01-01 DOI: 10.1142/s0219530521500160

Yuan Shen, Yannian Zuo, Liming Sun, Xiayang Zhang

{"title":"Modified proximal symmetric ADMMs for multi-block separable convex optimization with linear constraints","authors":"Yuan Shen, Yannian Zuo, Liming Sun, Xiayang Zhang","doi":"10.1142/s0219530521500160","DOIUrl":"https://doi.org/10.1142/s0219530521500160","url":null,"abstract":"We consider the linearly constrained separable convex optimization problem whose objective function is separable with respect to [Formula: see text] blocks of variables. A bunch of methods have been proposed and extensively studied in the past decade. Specifically, a modified strictly contractive Peaceman–Rachford splitting method (SC-PRCM) [S. H. Jiang and M. Li, A modified strictly contractive Peaceman–Rachford splitting method for multi-block separable convex programming, J. Ind. Manag. Optim. 14(1) (2018) 397-412] has been well studied in the literature for the special case of [Formula: see text]. Based on the modified SC-PRCM, we present modified proximal symmetric ADMMs (MPSADMMs) to solve the multi-block problem. In MPSADMMs, all subproblems but the first one are attached with a simple proximal term, and the multipliers are updated twice. At the end of each iteration, the output is corrected via a simple correction step. Without stringent assumptions, we establish the global convergence result and the [Formula: see text] convergence rate in the ergodic sense for the new algorithms. Preliminary numerical results show that our proposed algorithms are effective for solving the linearly constrained quadratic programming and the robust principal component analysis problems.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63880944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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: 1

Asymptotic expansions for Wiener–Hopf equations Wiener-Hopf方程的渐近展开式

IF 2.2 2区数学

Analysis and Applications Pub Date : 2020-12-08 DOI: 10.1142/s0219530520500207

Kui Li, R. Wong

引用次数: 1

Distributions of anisotropic order and applications to H-distributions 各向异性阶分布及其在h分布中的应用

IF 2.2 2区数学

Analysis and Applications Pub Date : 2020-11-30 DOI: 10.1142/S0219530520500165

N. Antonić, Marko Erceg, M. Mišur

引用次数: 5

Data informed solution estimation for forward-backward stochastic differential equations 前向-后向随机微分方程的数据知情解估计

IF 2.2 2区数学

Analysis and Applications Pub Date : 2020-10-19 DOI: 10.1142/s0219530520400102

F. Bao, Yanzhao Cao, J. Yong

引用次数: 3