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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence analysis of one-point large deviations rate functions of numerical methods for stochastic wave equations with small noise
小噪声 随机波动方程 数值方法 单点大偏差率 函数收敛分析
2023/4/21
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convergence Thery of Deep Neural Networks: Arbitrary Activation Functions and Pooling
深度神经网络 激活函数 池化
2023/4/28
Deep neural networks, as a powerful system to represent high dimensional complex functions, play a key role in deep learning. Convergence of deep neural networks is a fundamental issue in building the...
Convergence of frozen Gaussian approximation for high frequency wave propagation
Convergence of frozen Gaussian high frequency wave propagation
2011/2/25
The frozen Gaussian approximation provides a highly efficient computational method for high frequency wave propagation. The derivation of the method is based on asymptotic analysis. In this paper, fo...
Rainwater-Simons-type convergence theorems for generalized convergence methods
Rainwater-Simons-type convergence theorems generalized convergence methods
2010/11/17
We extend the well-known Rainwater-Simons convergence theorem to various generalized convergence methods such as strong matrix summability, statistical convergence and almost convergence. In fact we ...
On the convergence of Chebyshev--Padé approximations to real-valued algebraic functions
Chebyshev--Padé approximations real-valued algebraic functions
2010/12/13
В работе анонсируются новые результаты о сходимости аппроксимаций Чебышёва–
Паде для вещественных алгебраических функций, заданных на отрезке [−1, 1]. Скорость
сходимости аппроксимаций на отре...
Ergodic approximation of the distribution of a stationary diffusion : rate of convergence
stochastic differential equation stationary process steady regime ergodic diffusion Central Limit Theorem Euler scheme
2010/11/26
We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally e...
Convergence of Infinite Composition of Entire Functions
Infinite Composition Entire Functions
2010/12/6
The purpose of the present article is to obtain the condition that the function defined by infinite composition of entire functions be-comes an entire function. Moreover, as an example of such functio...
Rate of convergence of linear functions on the unitary group
Rate of convergence linear functions unitary group
2010/11/29
We study the rate of convergence to a normal random variable of the real and imaginary parts of TrANU, where U is an N ×N random unitary matrix and AN is a deterministic complex matrix.
Rate of Convergence and Tractability of the Radial Function Approximation Problem
Gaussian kernel reproducing kernel Hilbert spaces shape parameter
2011/1/21
This article studies the problem of approximating functions belonging to a Hilbert space Hd with an isotropic or anisotropic Gaussian reproducing kernel.
Convergence of Unbounded Multivalued Supermartingales in the Mosco and Slice Topologies
Unbounded Multivalued Supermartingales Mosco Slice Topologies
2009/1/22
Our starting point is the Mosco-convergence result due to Hess ([18]) for integrable multivalued supermartingales whose values may be unbounded, but are majorized by a $w$-ball-compact-valued function...
Painleve-Kuratowski convergence results are obtained, under sufficient conditions of minimal character, for approximate Nash equilibria of two sequences of real valued functions. Moreover, an applicat...
Memory Effects and $\boldsymbol{\Gamma}$-Convergence：A Time Dependent Case
Time Dependent Case Memory Effects $\boldsymbol{\Gamma}$-Convergence
2009/1/19
We study the asymptotic behavior of the energy functional associated to the parametric equation $\partial_t u_\varepsilon(t, x)$ $+ a_\varepsilon(t, x) g (u_\varepsilon(t, x)) =f(t, x)$, $u_\varepsil...
Epi-Distance Convergence of Parametrised Sums of Convex Functions in Non-Reflexive Spaces
Epi-Distance Convergence Parametrised Sums Convex Functions Non-Reflexive Spaces
2009/1/13
A weakened set of conditions is established for the epi-distance convergence of a sum $\{f_v+g_v\}_{v\in W}$ of parametrised closed convex functions $\{f_v\}_{v\in W}$ and $\{g_v\}_{v\in W}$ for $v\to...
Inequalities of Maximum of Partial Sums and Weak Convergence for a Class Weak Dependent Random Variables
$\rho^{-}$-mixing $\rho^{*}$-mixing NA rosenthal type inequalities weak convergence
2007/12/12
In this paper, we establish a Rosenthal-type inequality of the maximum of partial sums for $\rho^{-}$-mixing random fields. As its applications we get the H\'{a}jeck--R\`{e}nyi inequality and weak con...
Pointwise Convergence and Uniform Convergence of Wavelet Frams Series
Wavelet frame series Wavelet orthonormal basis Uniform onvergence Pointwise convergence
2007/12/12
Pointwise convergence and uniform convergence for wavelet frame series is a new topic. With the help of band-limited dual wavelet frames, this topic is first researched.