Related papers: Existence of a Limiting Distribution for the Binar…
In this paper, we consider distributed optimization design for resource allocation problems over weight-balanced graphs. With the help of singular perturbation analysis, we propose a simple sub-optimal continuous-time optimization…
Given a potential of pair interaction and a value of activity, one can consider the Gibbs distribution in a finite domain $\Lambda \subset \mathbb{Z}^d$. It is well known that for small values of activity there exist the infinite volume…
The Banach-Picard iteration is widely used to find fixed points of locally contractive (LC) maps. This paper extends the Banach-Picard iteration to distributed settings; specifically, we assume the map of which the fixed point is sought to…
We consider a diffusive model for optimally distributing dividends, while allowing for Knightian model ambiguity concerning the drift of the surplus process. We show that the value function is the unique solution of a non-linear…
In this paper we revisit the exsistence theorem for $L^r$-optimal quantization, $r\ge 2$, with respect to a Bregman divergence: we establish the existence of optimal quantizaers under lighter assumptions onthe strictly convex function which…
We introduce a class of one-dimensional discrete space-discrete time stochastic growth models described by a height function $h_t(x)$ with corner initialization. We prove, with one exception, that the limiting distribution function of…
A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and…
In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
In this paper, we prove the existence and uniqueness of solutions as well as ergodicity for McKean-Vlasov SDEs under Lyapunov conditions, in which the Lyapunov functions are defined on $\mathbb R^d\times \mathcal P_2(\mathbb R^d)$, i.e. the…
Certain extremum estimators have asymptotic distributions that are non-Gaussian, yet characterizable as the distribution of the $\argmax$ of a Gaussian process. This paper presents high-level sufficient conditions under which such…
In this paper, we propose a numerical method to uniformly handle the random genetic drift model for pure drift with or without natural selection and mutation. For pure drift and natural selection case, the Dirac $\delta$ singularity will…
This paper investigates the problem of finding a fixed point for a global nonexpansive operator under time-varying communication graphs in real Hilbert spaces, where the global operator is separable and composed of an aggregate sum of local…
This paper considers the regularized Tyler's scatter estimator for elliptical distributions, which has received considerable attention recently. Various types of shrinkage Tyler's estimators have been proposed in the literature and proved…
We introduce a new basic model for independent and identical distributed sequence on the canonical space $(\mathbb{R}^\mathbb{N},\mathcal{B}(\mathbb{R}^\mathbb{N}))$ via probability kernels with model uncertainty. Thanks to the well-defined…
We highlight a certain compactness of Sidon sets and $B_2[g]$-sets and provide several applications. Notably, we prove the existence of such sets that maximize certain functions. In particular, we show the existence of a Sidon set whose…
In the framework of Clifford analysis, a chain of harmonic and monogenic potentials in the upper half of (m+1)-dimensional Euclidean space was recently constructed, including a higher dimensional analogue of the logarithmic function in the…
In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…
We prove that the distributions defined on the Gelfand-Shilov spaces, and hence more singular than hyperfunctions, retain the angular localizability property. Specifically, they have uniquely determined support cones. This result enables…
This paper studies a Shannon-theoretic version of the generalized distribution preserving quantization problem where a stationary and memoryless source is encoded subject to a distortion constraint and the additional requirement that the…