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Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate non-local operator Green function Poisson kernel
2016/1/26
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
Using the Continuous Spectrum to “Feel” Integrability: the Effect of Boundary Conditions
Test model integrability partial differential differential difference equations of continuous spectrum
2014/12/29
The scope of this work is to propose a method for testing the integrability of a model partial differential (PDE) and/or differential difference equation (DDE). For monoparametric families of PDE/DDE’...
Determinantal probability densities at two-qubit separability-entanglement boundary and associated Fisher information
Determinantal probability densities two-qubit separability-entanglement boundary associated Fisher information
2013/4/28
The determinants (|rho^{PT}|) of the partial transposes of 4 x 4 density matrices (rho) have possible values in the interval [-1/16, 1/256], and are nonnegative if and only if rho is separable. In arX...
Behavior of Graph Laplacians on Manifolds with Boundary
Graph Laplacians Behavior Manifolds Boundary
2011/6/21
In manifold learning, algorithms based on graph Laplacians constructed from data have received
considerable attention both in practical applications and theoretical analysis. In particular, the
conv...
Optimal Multistage Sampling in a Boundary-Crossing Problem
Asymptotic Brownian motion Group sequential Multistage Optimality
2011/6/17
Brownian motion with known positive drift is sampled in stages until
it crosses a positive boundary a. A family of multistage samplers that con-
trol the expected overshoot over the boundary by vary...
Free boundary problem for controlled stochastic differential equations
Free boundary problem controlled stochastic differential equations
2009/9/24
Free boundary problem for controlled stochastic differential equations。
Bayesian Multivariate Areal Wombling for Multiple Disease Boundary Analysis
Arealdata Cancer Multivariateconditionally autoregressive(MCAR)model Surveillance Epidemiology and End Results (SEER) data
2009/9/22
Multivariate data summarized over areal units (counties, zip codes,
etc.) are common in the eld of public health. Estimation or testing of geo-
graphic boundaries for such data may have varied goals...
Estimates for the Poisson kernels on homogeneous manifolds of negative curvature and the boundary Harnack inequality in the noncoercive case
Estimates for the Poisson kernels homogeneous manifolds negative curvature the boundary Harnack inequality
2009/9/21
Using a probabilistic technique we obtain upper and
lower estimates for the Poisson kernels of the second order diflerential
operators on a homogeneous manifold of negative curvature. Our
results i...
Boundary Crossings of Brownian Motion
Brownian motion with trend boundary crossing probability large deviations
2009/4/27
Let B be a standard Brownian motion and let b_gamma be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of P{ B(t)< b_gamma(t), forall tin [0,1]} ...
Fixed Points of the Smoothing Transform：the Boundary Case
Fixed Points Smoothing Boundary Case
2009/4/8
Let $A=(A_1,A_2,A_3,ldots)$ be a random sequence of non-negative numbers that are ultimately zero with $E[sum A_i]=1$ and $E left[sum A_{i} log A_i right] leq 0$. The uniqueness of the non-negative fi...
Confidence Sets in Boundary and Set Estimation
random closed set oriented distance functions set expectation boundaryestimation level set simultaneous confidence interval
2010/3/18
Let p1 ≤ p2 and consider estimating a fixed set {x : p1 ≤ f(x) ≤ p2}
by the random set {x : p1 ≤ b fn(x) ≤ p2}, where b fn is a consistent estimator of
the continuous function f. This paper gives co...
