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This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
In general, comprehension of any type of complex system depends on the resolution used to examine the phenomena occurring within it. However, identifying a priori, for example, the best time frequencies/scales to study a certain system…
Time-series photometry and spectroscopy of transiting exoplanets allow us to study their atmospheres. Unfortunately, the required precision to extract atmospheric information surpasses the design specifications of most general purpose…
The continuous advances in data collection and storage techniques allow us to observe and record real-life processes in great detail. Examples include financial transaction data, fMRI images, satellite photos, earths pollution distribution…
This paper introduces a spatio-temporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatio-temporal data. The model is derived as a spatial extension of a stochastic harmonic…
Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent years. However, these models are used mainly as a statistical…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…
The quantum dense output problem is the process of evaluating time-accumulated observables from time-dependent quantum dynamics using quantum computers. This problem arises frequently in applications such as quantum control and…
Functional time series analysis, whether based on time of frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless,…
Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical…
Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…
Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Searches for statistically significant correlations between arrival directions of ultra-high energy cosmic rays and classes of astrophysical objects are common in astroparticle physics. We present a method to test potential correlation…
We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…
This paper proposes stochastic models for the analysis of ocean surface trajectories obtained from freely-drifting satellite-tracked instruments. The proposed time series models are used to summarise large multivariate datasets and infer…
Physiologic signals have properties across multiple spatial and temporal scales, which can be shown by the complexity-analysis of the coarse-grained physiologic signals by scaling techniques such as the multiscale. Unfortunately, the…