Related papers: Walsh Spider Diffusions as Time Changed Multi-para…
The time evolution of a bounded quantum system is considered in the framework of the orthogonal, unitary and symplectic circular ensembles of random matrix theory. For an $N$ dimensional Hilbert space we prove that in the large $N$ limit…
Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we…
The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the…
Solving multiscale diffusion problems is often computationally expensive due to the spatial and temporal discretization challenges arising from high-contrast coefficients. To address this issue, a partially explicit temporal splitting…
We study a majority based preference diffusion model in which the members of a social network update their preferences based on those of their connections. Consider an undirected graph where each node has a strict linear order over a set of…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
We propose an online algorithm for tracking a multidimensional time-varying parameter of a time series, which is also allowed to be a predictable process with respect to the underlying time series. The algorithm is driven by a gain…
Physical models with uncertain inputs are commonly represented as parametric partial differential equations (PDEs). That is, PDEs with inputs that are expressed as functions of parameters with an associated probability distribution.…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…
Training diffusion models is always a computation-intensive task. In this paper, we introduce a novel speed-up method for diffusion model training, called, which is based on a closer look at time steps. Our key findings are: i) Time steps…
A distributed adaptive algorithm is proposed to solve a node-specific parameter estimation problem where nodes are interested in estimating parameters of local interest, parameters of common interest to a subset of nodes and parameters of…
We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion…
A continuous time mixed state branching process is constructed as the scaling limits of two-type Galton-Watson processes. The process can also be obtained by the pathwise unique solution to a stochastic equation system. From the stochastic…
Given a heterogeneous time-series sample, the objective is to find points in time (called change points) where the probability distribution generating the data has changed. The data are assumed to have been generated by arbitrary unknown…
This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to…
We consider the diffusion scaling limit of the one-dimensional vicious walker model of Fisher and derive a system of nonintersecting Brownian motions. The spatial distribution of $N$ particles is studied and it is described by use of the…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…