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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arbitrarily high-order cut-off methods to preserve maximum bound principle for Allen-Cahn equations
Allen-Cahn equations 最大界限原理 任意高阶 截止方法
2023/4/14
A new class of high-order maximum principle preserving numerical methods is proposed for solving the semilinear Allen-Cahn equation. We start with the method consists of a $k$th-order multistep expone...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations principle for weighted means of a recursive numerical method for ergodic SDEs
遍历 SDE递归 数值方法 加权均值 大偏差原理
2023/4/24
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Large deviations in random interlacements I: Large deviation principle of occupation measures
随机交错 大偏差 占用措施 大偏差原则
2023/5/10
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boltzmann-Gibbs principle in L^p sense via Littlewood-Paley-Stein inequality
L^p意义 玻尔兹曼-吉布斯原理 利特尔伍德-佩利-斯坦不等式
2023/5/15
KPZ limit for one-dimensional weakly asymmetric Ginzburg-Landau model was studied by Diehl-Gubinelli-Perkowski in a setting of martingale (energy) solution. Our goal is to apply a path-wise approach b...
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS,GRAPHS AND METRIC MEASURE SPACES
Uncertainty principle p.c.f. fractal Heisenberg’s inequality measure metric spaces Poincar′ e inequality self-similar graphs Sierpinski ′ gasket uniform finitely ramified graphs
2015/12/10
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Averaging principle for quasi-linear parabolic PDE’s and related diffusion processes
Quasi linear disturbance two dimensional flow parabola and small parameter
2015/9/28
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
A dinner table seats k guests and holds n discrete morsels of food. Guests select morsels in turn until all are consumed. Each guest has a ranking of the morsels according to how much he would enjoy e...
A moderate deviation principle for empirical bootstrap measure
Large deviations moderate deviations bootstrap empirical measure
2012/6/27
We establish two moderate deviation principles (MDP) in the bootstrap setting. We prove MDP for the joint distribution of the empirical measure and the empirical bootstrap measure (empirical measure o...
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations
Dynamic programming principle stochastic games Isaacs equation
2012/5/9
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a...
On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains
Dynamic programming principle stochastic games Isaacs equation
2012/5/9
We prove the dynamic programming principe for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a...
Typically, models with a heterogeneous property are considerably harder to analyze than the corresponding homogeneous models, in which the heterogeneous property is replaced with its average value. In...
Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space
Random metric space random normed module L0− valued function lower semicontinuity Ekeland’s variational principle
2011/9/20
Abstract: Motivated by the recent work on conditional risk measures, this paper studies the Ekeland's variational principle for a proper, lower semicontinuous and lower bounded $\bar{L}^{0}-$valued fu...
Moderate Deviation Principle for dynamical systems with small random perturbation
Freidlin-Wentzell’s theorem large deviations moderate deviations Talagrand’s transportation inequality
2011/9/14
Abstract: Consider the stochastic differential equation in $\rr^d$
dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t
X^{\e}_0&=x_0,\quad x_0\in\rr^d
where $b:\rr^d\rightarrow\rr^d$ is $C^1$ s...
On the minimal set for counterexamples to the local-global principle
minimal set counterexamples local-global principle Number Theory
2011/9/14
Abstract: We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous cri...