相关论文: An algebraic approach to Polya processes

We introduce a simple model which shows non-trivial self organized critical properties. The model describes a system of interacting units, modelled by Polya urns, subject to perturbations and which occasionally break down. Three equivalent…

Consider a classical elliptic pseudodifferential operator $P$ on ${\Bbb R}^n$ of order $2a$ ($0<a<1)$ with even symbol. For example, $P=A(x,D)^a$ where $A(x,D)$ is a second-order strongly elliptic differential operator; the fractional…

Sampling from a random discrete distribution induced by a `stick-breaking' process is considered. Under a moment condition, it is shown that the asymptotics of the sequence of occupancy numbers, and of the small-parts counts (singletons,…

In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dY_{s}^{(1)}$% , where $u$ is a $\beta$-H\"older continuous process with $\beta > 1-H$ and…

Fractional Poisson processes, a rapidly growing area of non-Markovian stochastic processes, are useful in statistics to describe data from counting processes when waiting times are not exponentially distributed. We show that the fractional…

We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…

Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…

Starting from the moment sequences of classical orthogonal polynomials we derive the orthogonality purely algebraically. We consider also the moments of ($q=1$) classical orthogonal polynomials, and study those cases in which the…

We use techniques from finite free probability to analyze matrix processes related to eigenvalues, singular values, and generalized singular values of random matrices. The models we use are quite basic and the analysis consists entirely of…

We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…

We consider a generalization of polynomial programs: algebraic programs, which are optimization or feasibility problems with algebraic objectives or constraints. Algebraic functions are defined as zeros of multivariate polynomials. They are…

By a symbolic method, we introduce multivariate Bernoulli and Euler polynomials as powers of polynomials whose coefficients involve multivariate L\'evy processes. Many properties of these polynomials are stated straightforwardly thanks to…

We develop a (co)algebraic framework to study a family of process calculi with monadic branching structures and recursion operators. Our framework features a uniform semantics of process terms and a complete axiomatisation of semantic…

P\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with…

A semi-process is an analog of the semi-flow for non-autonomous differential equations or inclusions. We prove an abstract result on the existence of measurable semi-processes in the situations where there is no uniqueness. Also, we allow…

This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…

Asymptotic notations are heavily used while analysing runtimes of algorithms. Present paper argues that some of these usages are non trivial, therefore incurring errors in communication of ideas. After careful reconsidera- tion of the…

The paper is devoted to a study of phase transitions in the Hermitian random matrix models with a polynomial potential. In an alternative equivalent language, we study families of equilibrium measures on the real line in a polynomial…

We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order…

We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…