相关论文: An Intuitive Approach to the Martin Boundary
A complete representation of the Martin boundary of killed random walks on a half-space $\Z^{d-1}\times\N^*$ is obtained. In particular, it is proved that the corresponding Martin boundary is homemorphic to the half-sphere ${\cal S}^d_+ =…
Using the Fitzpatrick function, we characterize the solutions for different classes of deterministic and stochastic differential equations driven by maximal monotone operators (or in particular subdifferential operators) as the minimum…
Many circumstances of practical importance have performance or success metrics which exist implicitly---in the eye of the beholder, so to speak. Tuning aspects of such problems requires working without defined metrics and only considering…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
In this article, we present the best possible upper and lower bounds for the Neuman-S\'andor mean in terms of the geometric combinations of harmonic and quadratic means, geometric and quadratic means, harmonic and contra-harmonic means, and…
The Martin boundary associated with the simple random walk on an example of partially oriented lattice is shown to be trivial by computing fine estimates of the Green kernel.
This survey gives an introduction to monetary measures of risk as monotone and cash additive functions on spaces of univariate random variables. Primal and dual representation results as well as several examples are discussed. Principal…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature,…
In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.
We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…
Generic Hamiltonian systems have a mixed phase space, where classically disjoint regions of regular and chaotic motion coexist. We present an iterative method to construct an integrable approximation, which resembles the regular dynamics of…
In this work we propose a new kind of parameterized outer estimate of the united solution set to an interval parametric linear system. The new method has several advantages compared to the methods obtaining parameterized solutions…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
This paper is dedicated to the analysis and detailed study of a procedure to generate both the weighted arithmetic and harmonic means of $n$ positive real numbers. Together with this interpretation, we prove some relevant properties that…
The theory of modular forms and spherical harmonic analysis are applied to establish new best bounds towards the counting and equidistribution of rational points on spheres and other higher dimensional ellipsoids, in what may be viewed as a…
We illustrate the power of Experimental Mathematics and Symbolic Computation to suggest irrationality proofs of natural constants, and the determination of their irrationality measures. Sometimes such proofs can be fully automated, but…
Despite the growing body of work in interpretable machine learning, it remains unclear how to evaluate different explainability methods without resorting to qualitative assessment and user-studies. While interpretability is an inherently…
Conceptual blending is a powerful tool for computational creativity where, for example, the properties of two harmonic spaces may be combined in a consistent manner to produce a novel harmonic space. However, deciding about the importance…
In this paper we consider non-compact non-flat simply connected harmonic manifolds. In particular, we show that the Martin boundary and Busemann boundary coincide for such manifolds. For any finite volume quotient we show that (up to…