Related papers: Time-consistent conditional expectation under prob…
This study examines statistical performance of tests for time-varying properties under misspecified conditional mean and variance. When we test for time-varying properties of the conditional mean in the case in which data have no…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
We show how rate-distortion theory provides a mechanism for automated theory building by naturally distinguishing between regularity and randomness. We start from the simple principle that model variables should, as much as possible, render…
In this paper we extend the definition of time conditional G-expectations $\mathbb{\hat{E}}_{t}[\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time…
We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 1<z<6. We find that the perturbation theory prediction agrees with the simulations to better…
We develop a general framework for the identification of counterfactual parameters in a class of nonlinear semiparametric panel models with fixed effects and time effects. Our method applies to models for discrete outcomes (e.g., two-way…
We justify and discuss expressions for joint lower and upper expectations in imprecise probability trees, in terms of the sub- and supermartingales that can be associated with such trees. These imprecise probability trees can be seen as…
Systems are commonly monitored for health and security through collection and streaming of multivariate time series. Advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
Within the framework of the cumulative prospective theory of Kahneman and Tversky, this paper considers a continuous-time behavioral portfolio selection problem whose model includes both running and terminal terms in the objective…
Several procedures have been recently proposed to test the simplifying assumption for conditional copulas. Instead of considering pointwise conditioning events, we study the constancy of the conditional dependence structure when some…
Most previous contributions to BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to…
For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we…
Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have…
Recently, in the paper: T. Koszto{\l}owicz and A. Dutkiewicz, Phys. Rev. E \textbf{104}, 014118 (2021) the $g$--subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ has been considered. This…
Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising…
We prove existence and uniqueness for some nonlinear stochastic differential equation used in molecular dynamics, whose nonlinearity comes from a conditional expectation term. We also introduce an interacting particle system in order to…
In this work we propose a different surgical modified model for the construction of counterfactual variables under non parametric structural equation models. This approach allows the simultaneous representation of counterfactual responses…
Systems with stochastic time delay between the input and output present a number of unique challenges. Time domain noise leads to irregular alignments, obfuscates relationships and attenuates inferred coefficients. To handle these…
Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional…