Related papers: Infinite dimensional affine processes
The purpose of this paper is to provide equations to model the evolution of effective diffusion over a Riemannian fiber bundle (under the hypothesis of infinite diffusion rate along compact fibers). These equations are obtained by…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We develop a method for calculating the persistence landscapes of affine fractals using the parameters of the corresponding transformations. Given an iterated function system of affine transformations that satisfies a certain compatibility…
The aim of this article is to construct solutions to second order in time stochastic partial differential equations and to show hypocoercivity of the corresponding transition semigroups. More generally, we analyze non-linear…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
Anomalous diffusion is a common phenomenon observed in underground solute transport, soil water infiltration and sediment movement, etc. Time and space fractional derivative advection-dispersion equation (FADE) has been widely employed as…
We give an account of matter and (basically) a solution of a new class of problems synthesizing percolation theory and branching diffusion processes. They led us to realizing a novel type of stochastic processes, namely branching processes…
We consider the filtering and smoothing problems for an infinite-dimensional diffusion process X, observed through a finite-dimensional representation at discrete points in time. At the heart of our proposed methodology lies the…
For reaction-diffusion processes without exclusion, in which the particles can exist in the same site of a one-dimensional lattice, we study all the integrable models which can be obtained by imposing a boundary condition on the master…
We prove that joint uniqueness in law and the existence of a strong solution imply pathwise uniqueness for variational solutions to stochastic partial differential equations of the form \begin{align*}…
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a…
We consider a reaction-diffusion system which may serve as a model for a ferment catalytic reaction in chemistry. The model consists of a system of reaction diffusion equations with unbounded time dependent coefficients and different…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of weak Dirichlet process in this context. Such a process X, taking…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of "weak Dirichlet process" in this context. Such a process $\X$,…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Matrix-valued stochastic processes have been of significant importance in areas such as physics, engineering and mathematical finance. One of the first models studied has been the so-called Wishart process, which is described as the…
This paper introduces $\infty$-Diff, a generative diffusion model defined in an infinite-dimensional Hilbert space, which can model infinite resolution data. By training on randomly sampled subsets of coordinates and denoising content only…
Affine point processes are a class of simple point processes with self- and mutually-exciting properties, and they have found useful applications in several areas. In this paper, we obtain large-time asymptotic expansions in large…
We focus on a branch of region-based spatial logics dealing with affine geometry. The research on this topic is scarce: only a handful of papers investigate such systems, mostly in the case of the real plane. Our long-term goal is to…