Related papers: Statistical Modeling for Spatio-Temporal Data from…
A study on the notion of covariant derivatives in flat and curved space-time via It\^o-Wiener processes, when subjected to stochastic processes, is presented. Going into details, there is an analysis of the following topics: (i) Besov…
Advances in Geographical Information Systems (GIS) have led to the enormous recent burgeoning of spatial-temporal databases and associated statistical modeling. Here we depart from the rather rich literature in space-time modeling by…
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…
It is shown how Adler's trace dynamics can be applied to stochastic mechanics and other complex classical dynamical systems. Emergent non-commutivity due to the fractal nature of sample trajectories is closely related to the fact that the…
In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function…
In many problem settings that require spatio-temporal forecasting, the values in the time-series not only exhibit spatio-temporal correlations but are also influenced by spatial diffusion across locations. One such example is forecasting…
Missing data in spatiotemporal systems presents a significant challenge for modern applications, ranging from environmental monitoring to urban traffic management. The integrity of spatiotemporal data often deteriorates due to hardware…
Time-dependent conformal maps are used to model a class of growth phenomena limited by coupled non-Laplacian transport processes, such as nonlinear diffusion, advection, and electro-migration. Both continuous and stochastic dynamics are…
In applications like environment monitoring and pollution control, physical quantities are modeled by spatio-temporal fields. It is of interest to learn the statistical distribution of such fields as a function of space, time or both. In…
Spatiotemporal (ST) data collected by sensors can be represented as multi-variate time series, which is a sequence of data points listed in an order of time. Despite the vast amount of useful information, the ST data usually suffer from the…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval…
Statistic modeling and data-driven learning are the two vital fields that attract many attentions. Statistic models intend to capture and interpret the relationships among variables, while data-based learning attempt to extract information…
Many real-world systems modeled using partial differential equations (PDEs) involve unknown parameters that must be estimated from limited, noisy system observations. While typically assumed to be constants, some of these unobserved…
In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
We present a method for the identification of continuous, spatiotemporal dynamics from experimental data. We use a model in the form of a partial differential equation and formulate an optimization problem for its estimation from data. The…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…