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Einstein realised that the fluctuations of a Brownian particle can be used to ascertain properties of its environment. A large number of experiments have since exploited the Brownian motion of colloidal particles for studies of dissipative…

We consider a system of diffusing particles on the real line in a quadratic external potential and with repulsive electrostatic interaction. The empirical measure process is known to converge weakly to a deterministic measure-valued process…

Accurate sensor placement is critical for modeling spatio-temporal systems such as environmental and climate processes. Neural Processes (NPs), particularly Convolutional Conditional Neural Processes (ConvCNPs), provide scalable…

We propose a metric space of coalescing pairs of paths on which we are able to prove (more or less) directly convergence of objects such as the persistence probability in the (one dimensional, nearest neighbor, symmetric) voter model or the…

We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general…

Human motion prediction is an important and challenging topic that has promising prospects in efficient and safe human-robot-interaction systems. Currently, the majority of the human motion prediction algorithms are based on deterministic…

This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…

The quest for precision in parameter estimation is a fundamental task in different scientific areas. The relevance of this problem thus provided the motivation to develop methods for the application of quantum resources to estimation…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…

Closed-form, interpretable mathematical models have been instrumental for advancing our understanding of the world; with the data revolution, we may now be in a position to uncover new such models for many systems from physics to the social…

We show that density models describing multiple observables with (i) hard boundaries and (ii) dependence on external parameters may be created using an auto-regressive Gaussian mixture model. The model is designed to capture how observable…

The paper studies asymptotic properties of estimators of multidimensional stochastic differential equations driven by Brownian motions from high-frequency discrete data. Consistency and central limit properties of a class of estimators of…

In the manufacturing process, sensor data collected from equipment is crucial for building predictive models to manage processes and improve productivity. However, in the field, it is challenging to gather sufficient data to build robust…

The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…

This article deals with the numerical resolution of backward stochastic differential equations. Firstly, we consider a rather general case where the filtration is generated by a Brownian motion and a Poisson random measure. We provide a…

In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…

This article addresses the issue of estimating observation parameters (response and error parameters) in inverse problems. The focus is on cases where regularization is introduced in a Bayesian framework and the prior is modeled by a…