Related papers: Uncertain Data in Initial Boundary Value Problems:…

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…

A causal query will commonly not be identifiable from observed data, in which case no estimator of the query can be contrived without further assumptions or measured variables, regardless of the amount or precision of the measurements of…

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…

We study whether the solutions of a parabolic equation with diffusion given by the fractional Laplacian and a dominating gradient term satisfy Dirichlet boundary data in the classical sense or in the generalized sense of viscosity…

Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…

A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a set of singular functions are identified which match certain…

We consider an initial mixed-boundary value problem for anisotropic fractional type degenerate parabolic equations posed in bounded domains. Namely, we consider that the boundary of the domain splits into two parts. In one of them, we…

We consider conservation laws with source terms in a bounded domain with Dirichlet boundary conditions. We first prove the existence of a strong trace at the boundary in order to provide a simple formulation of the entropy boundary…

Untrained large neural networks, just after random initialization, tend to favour a small subset of classes, assigning high predicted probabilities to these few classes and approximately zero probability to all others. This bias, termed…

Learning models or control policies from data has become a powerful tool to improve the performance of uncertain systems. While a strong focus has been placed on increasing the amount and quality of data to improve performance, data can…

As the world increasingly relies on mathematical models for forecasts in different areas, effective communication of uncertainty in time series predictions is important for informed decision making. This study explores how users estimate…

We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We…

Missing values are common in photovoltaic (PV) power data, yet the uncertainty they induce is not propagated into predictive distributions. We develop a framework that incorporates missing-data uncertainty into short-term PV forecasting by…

We consider the initial boundary value problem of non-homogeneous stochastic heat equation. The derivative of the solution with respect to time receives heavy random perturbation. The space boundary is Lipschitz and we impose non-zero…

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…

The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot…

This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend…

We establish well-posedness of initial-boundary value problems for continuity equations with BV (bounded total variation) coefficients. We do not prescribe any condition on the orientation of the coefficients at the boundary of the domain.…

Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…