Related papers: A Causal Construction of Diffusion Processes
This paper begins by giving an historical context to fractional Brownian Motion and its development. Section 2 then introduces the fractional calculus, from the Riemann-Liouville perspective. In Section 3, we introduce Brownian motion and…
In this note we analyse the propagation of a small density perturbation in a one-dimensional compressible fluid by means of fractional calculus modelling, replacing thus the ordinary time derivative with the Caputo fractional derivative in…
In this paper we detail the mechanisms that drive substitutional binary diffusion and derive appropriate governing equations. We focus on the one-dimensional case with insulated boundary conditions. Asymptotic expansions are used in order…
For a given thermodynamic system, and a given choice of coarse-grained state variables, the knowledge of a force-flux constitutive law is the basis for any nonequilibrium modeling. In the first paper of this series we established how, by a…
An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…
Weakly nonlinear amplitude equations are derived for the onset of spatially extended patterns on a general class of n-component bulk-surface reaction-diffusion systems in a ball, under the assumption of linear kinetics in the bulk and…
Despite the success of fractional Brownian motion (fBm) in modeling systems that exhibit anomalous diffusion due to temporal correlations, recent experimental and theoretical studies highlight the necessity for a more comprehensive approach…
Stationary distributions of multivariate diffusion processes have recently been proposed as probabilistic models of causal systems in statistics and machine learning. Motivated by these developments, we study stationary multivariate…
A Fokker-Planck equation approach for the treatment of non-Markovian stochastic processes is proposed. The approach is based on the introduction of fictitious trajectories sharing with the real ones their local structure and initial…
Aims. Numerical test-particle simulations are a reliable and frequently used tool to test analytical transport theories and to predict mean-free paths. The comparison between solutions of the diffusion equation and the particle flux is used…
Causal Models are like Dependency Graphs and Belief Nets in that they provide a structure and a set of assumptions from which a joint distribution can, in principle, be computed. Unlike Dependency Graphs, Causal Models are models of…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
The aim of this paper is to discuss a recent result which shows that probabilistic inference in the presence of (unknown) causal mechanisms can be tractable for models that have traditionally been viewed as intractable. This result was…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…
The inference of causal relationships among observed variables is a pivotal, longstanding problem in the scientific community. An intuitive method for quantifying these causal links involves examining the response of one variable to…
In the path integral formulation of the evolution of an open quantum system coupled to a Gaussian, non-interacting environment, the dynamical contribution of the latter is encoded in an object called the influence functional. Here, we…
Of primary interest in this paper is the numerical approximation of a time dependent fractional, in space, diffusion equation where the domain is assumed to be nonhomogeneous, having different axial diffusion coefficients. This work is…
We investigate a functional obtained by summing the squared differences of the integral of an Ito process over disjoint intervals. The limit of this sum is shown to converge in probability to two thirds the quadratic variation of the…
We derive an Ito-formula for the Dawson-Watanabe superprocess, a well-known class of measure-valued processes, extending the classical Ito-formula with respect to two aspects. Firstly, we extend the state-space of the underlying process…