相关论文: Infinitely divisible distributions over locally co…

We study the connections between volume growth, spectral properties and stochastic completeness of locally finite graphs. For a class of graphs with a very weak spherical symmetry we give a condition which implies both stochastic…

The Airy process is characterized by its finite-dimensional distribution functions. We show that each finite-dimensional distribution function is expressible in terms of a solution to a system of differential equations.

In this note several computations of equivariant cohomology groups are performed. For the compactly supported equivariant cohomology, the notion of infinitesimal index developed in arXiv:1003.3525, allows to describe these groups in terms…

We consider a countable system of interacting (possibly non-Markovian) stochastic differential equations driven by independent Brownian motions and indexed by the vertices of a locally finite graph $G = (V,E)$. The drift of the process at…

We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as…

We study the finite dimensional partition properties of the countable homogeneous dense local order. Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of…

In this short note we present several infinite dimensional theorems which generalize corresponding facts from the finite dimensional differential inclusions theory.

The function spaces of continuously differentiable functions are extensively studied and appear in various mathematical settings. In this context, we investigate the spaces of continuously fractional differentiable functions of order…

We investigate the distribution and multiple occurrences of extreme events stochastic processes constructed by sampling the solution of a Stochastic Differential Equation on $\mathbb{R}^n$. We do so by studying the action of an annealead…

We study a system of stochastically forced infinite-dimensional coupled harmonic oscillators. Although this system formally conserves energy and is not explicitly dissipative, we show that it has a nontrivial invariant probability measure.…

We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in…

In this paper, we introduce the notions of a vector-valued almost automorphic distribution and a vector-valued almost automorphic ultradistribution, working in the framework of complex Banach spaces. We prove several structural…

We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…

In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…

We consider the infinite divisibility of distributions of some well-known inverse subordinators. Using a tail probability bound, we establish that distributions of many of the inverse subordinators used in the literature are not infinitely…

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…

For various classes of Lipschitz functions we provide dimension free concentration inequalities for infinitely divisible random vectors with independent components and finite exponential moments.

We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…

Inspired by R. Speicher's multidimensional free central limit theorem and semicircle families, we prove an infinite dimensional compound Poisson limit theorem in free probability, and define infinite dimensional compound free Poisson…

A probability distribution is n-divisible if its nth convolution root exists. While modeling the dependence structure between several (re)insurance losses by an additive risk factor model, the infinite divisibility, that is the…