Related papers: Stochastic analysis for the Dirichlet--Ferguson pr…

In this Ph.D. dissertation (2018, Emory University) we prove theorems at the intersection of the additive and multiplicative branches of number theory, bringing together ideas from partition theory, $q$-series, algebra, modular forms and…

The Doi-Peliti method is effective for investigating classical stochastic processes, and it has wide applications, including field theoretic approaches. Furthermore, it is applicable not only to master equations but also to stochastic…

In this paper, we propose a new comparison tool for spatial homogeneity of point processes, based on the joint examination of void probabilities and factorial moment measures. We prove that determinantal and permanental processes, as well…

We provide a general theorem bounding the error in the approximation of a random measure of interest--for example, the empirical population measure of types in a Wright-Fisher model--and a Dirichlet process, which is a measure having…

Quasidiffusion is an extension of regular diffusion which can be described as a Feller process on $\mathbb{R}$ with infinitesimal operator $L=\frac{1}{2}D_mD_s$. Here, $s(x) = x$ and $m$ refers to the (not necessarily fully supported) speed…

The chaos expansion of a general non-linear function of a Gaussian stationary increment process conditioned on its past realizations is derived. This work combines Wiener chaos expansion approach to study the dynamics of a stochastic system…

Cumulants of a fluctuating current can be obtained from a free energy-like generating function which for Markov processes equals the largest eigenvalue of a generalized generator. We determine this eigenvalue with the DMRG for stochastic…

We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an…

The updated version of the Helac-Phegas event generator is presented. The matrix elements are calculated through Dyson-Schwinger recursive equations. Helac-Phegas generates parton-level events with all necessary information, in the most…

This paper is devoted the the study of the mean field limit for many-particle systems undergoing jump, drift or diffusion processes, as well as combinations of them. The main results are quantitative estimates on the decay of fluctuations…

We provide a general construction scheme for $\mathcal L^p$-strong Feller processes on locally compact separable metric spaces. Starting from a regular Dirichlet form and specified regularity assumptions, we construct an associated…

We identify stationary distributions of generalized Fleming-Viot processes with jump mechanisms specified by certain beta laws together with a parameter measure. Each of these distributions is obtained from normalized stable random measures…

Inspired by a result of Soundararajan, assuming the Riemann hypothesis (RH), we prove a new inequality for the logarithm of the modulus of the Riemann zeta-function on the critical line in terms of a Dirichlet polynomial over primes and…

We deal with some extensions of the space-fractional diffusion equation, which is satisfied by the density of a stable process (see Mainardi, Luchko, Pagnini (2001)): the first equation considered here is obtained by adding an exponential…

We formulate dynamical rate equations for physical processes driven by a combination of diffusive growth, size fragmentation and fragment coagulation. Initially, we consider processes where coagulation is absent. In this case we solve the…

We study perturbation theory in certain quantum mechanics problems in which the perturbing potential diverges at some points, even though the energy eigenvalues are smooth functions of the coefficient of the potential. We discuss some of…

It is shown that for a non-decreasing self-similar stochastic process $T$ with independent increments, the range of $T$ forms a Poisson point process with $\sigma$-finite intensity if and only if the one-dimensional distribution of $T(1)$…

Although introduced in the case of Poisson random measures, the lent particle method applies as well in other situations. We study here the case of marked point processes. In this case the Malliavin calculus (here in the sense of Dirichlet…

We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is…

We propose a general approach for quantitative convergence analysis of non-reversible Markov processes, based on the concept of second-order lifts and a variational approach to hypocoercivity. To this end, we introduce the flow Poincar{\'e}…