Related papers: Hyper-positive definite functions I: scalar case, …

The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…

We prove a stochastic homogenization result for integral functionals defined on finite partitions assuming the surface tension to be stationary and possibly ergodic. We also consider the convergence of boundary value problems when we impose…

For a branching process in random environment it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the…

We establish the existence and the pointwise bound of the fundamental solution for the stationary Stokes system with measurable coefficients in the whole space $\mathbb{R}^d$, $d \ge 3$, under the assumption that weak solutions of the…

We study the existence of algebras of hypercyclic vectors for weighted backward shifts on sequence spaces of directed trees with the coordinatewise product. When $V$ is a rooted directed tree, we show the set of hypercyclic vectors of any…

Word representations induced from models with discrete latent variables (e.g.\ HMMs) have been shown to be beneficial in many NLP applications. In this work, we exploit labeled syntactic dependency trees and formalize the induction problem…

Enhancing a recent result of Bayart and Ruzsa we obtain a Birkhoff-type characterization of upper frequently hypercyclic operators and a corresponding Upper Frequent Hypercyclicity Criterion. As an application we characterize upper…

We study functional stochastic differential equations with a locally unbounded, functional drift focusing on well-posedness, stability and the strong Feller property. Following the non-functional case, we only consider integrability…

Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as well as normal ideals on a tree, and we characterize…

This paper discusses a special class of nonlinear Hawkes processes, where the rate function is the exponential function. We call these processes loglinear Hawkes processes. In the main theorem, we give sufficient conditions for explosion…

We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…

The definition of a holomorphic function over a general measurable space $S$ endowed with a Markov process is defined by Zeghib and Barre. In this article we consider holomorphic functions over graphs whose ranges are a given finite field…

Using generating functions techniques we develop a relation between the Hausdorff and spectral dimension of trees with a unique infinite spine. Furthermore, it is shown that if the outgrowths along the spine are independent and identically…

Multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that would enable extracting the so-called spectrum of singularities. In this paper we…

Decision tree learning is increasingly being used for pointwise inference. Important applications include causal heterogenous treatment effects and dynamic policy decisions, as well as conditional quantile regression and design of…

This work builds on the notion of record of rooted trees. We provide an alternative definition of parking functions, derive from it a record-preserving bijection between rooted trees and parking functions, and establish a join…

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…

We provide an effective classification of postcritically finite polynomials as dynamical systems by means of Hubbard Trees. This can be viewed as an application of the results developed in part 1 (Stony Brook IMS 1993/5).

We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of…

Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…