Related papers: Probability measure-valued polynomial diffusions

We show, for a class of discrete Fleming-Viot (or Moran) type particle systems, that the convergence to the equilibrium is exponential for a suitable Wassertein coupling distance. The approach provides an explicit quantitative estimate on…

This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…

In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…

The joint moments of the derivatives of the characteristic polynomial of a random unitary matrix, and also a variant of the characteristic polynomial that is real on the unit circle, in the large matrix size limit, have been studied…

The Fleming-Viot (FV) process is a measure-valued diffusion that models the evolution of type frequencies in a countable population which evolves under resampling (genetic drift), mutation, and selection. In the classic FV model the fitness…

In this paper, we establish several local and global gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques.

The behaviour of many dynamic real phenomena shows different phases, with each one following a sigmoidal type pattern. This requires studying sigmoidal curves with more than one inflection point. In this work, a diffusion process is…

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…

The Fleming-Viot process describes a system of $N$ particles diffusing on a graph with an absorbing site. Whenever one of the particles is absorbed, it is replaced by a new particle at the position of one of the $N-1$ remaining particles.…

Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…

Second order recurrence of a $d$-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities is established under suitable conditions. The…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

The probabilities for gaps in the eigenvalue spectrum of finite $ N\times N $ random unitary ensembles on the unit circle with a singular weight, and the related hermitian ensembles on the line with Cauchy weight, are found exactly. The…

Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external…

In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…

We characterize probability measure with finite moment of any order in terms of the symmetric difference operators of their Fourier transforms. By using our new characterization, we prove the continuity $f(t,v)\in C((0, \infty),L^1_{2k-2…

In this paper, we give a uniqueness result to a transport equation fulfilled by probability measure on a infinite dimensional Hilbert space. Main arguments are based on projective aspects and a probabilistic representation of the solutions.…

We propose a probabilistic derivation of the so-called chemical diffusion master equation (CDME) and describe an infinite dimensional moment generating function method for finding its analytical solution. CDMEs model by means of an infinite…

We consider predictive inference using a class of temporally dependent Dirichlet processes driven by Fleming--Viot diffusions, which have a natural bearing in Bayesian nonparametrics and lend the resulting family of random probability…

Score-based diffusion models have emerged as powerful techniques for generating samples from high-dimensional data distributions. These models involve a two-phase process: first, injecting noise to transform the data distribution into a…