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Comparison and converse comparison theorems are important parts of the research on backward stochastic differential equations. In this paper, we obtain comparison results for one dimensional backward stochastic differential equations with…
We consider nonparametric estimation for functional autoregressive processes with Markov switching. First, we study the case where complete data is available; i.e. when we observe the Markov switching regime. Then we estimate the regression…
This paper investigates the role of high-dimensional information sets in the context of Markov switching models with time varying transition probabilities. Markov switching models are commonly employed in empirical macroeconomic research…
Extreme Learning Machine (ELM) is an efficient and effective least-square-based learning algorithm for classification, regression problems based on single hidden layer feed-forward neural network (SLFN). It has been shown in the literature…
Charged particle dynamics under the influence of electromagnetic fields is a challenging spatiotemporal problem. Many high performance physics-based simulators for predicting behavior in a charged particle beam are computationally…
Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models…
When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This can be done by considering as basic uncertainty models the so-called credal sets that…
We explore a method of statistical estimation called Maximum Entropy on the Mean (MEM) which is based on an information-driven criterion that quantifies the compliance of a given point with a reference prior probability measure. At the core…
Forward-backward methods are a very useful tool for the minimization of a functional given by the sum of a differentiable term and a nondifferentiable one and their investigation has experienced several efforts from many researchers in the…
In this study we construct a time-space finite element (FE) scheme and furnish cost-efficient approximations for one-dimensional multi-term time fractional advection diffusion equations on a bounded domain $\Omega$. Firstly, a fully…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
In this work, we present a study combining two approaches in the context of solving PDEs: the continuous finite element method (FEM) and more recent techniques based on neural networks. In recent years, physics-informed neural networks…
Inverse parameter estimation of process-based models is a long-standing problem in many scientific disciplines. A key question for inverse parameter estimation is how to define the metric that quantifies how well model predictions fit to…
In this paper we derive stochastic representations for the finite dimensional distributions of a multidimensional diffusion on a fixed time interval, conditioned on the terminal state. The conditioning can be with respect to a fixed point…
Recently, the explicit constraint force method (ECFM) was introduced as a principled approach to solution reconstruction in the presence of missing physics. In solution reconstruction, parameters of a physical model are estimated from…
Exponential tilting is a technique commonly used in fields such as statistics, probability, information theory, and optimization to create parametric distribution shifts. Despite its prevalence in related fields, tilting has not seen…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
Generalising the idea of the classical EM algorithm that is widely used for computing maximum likelihood estimates, we propose an EM-Control (EM-C) algorithm for solving multi-period finite time horizon stochastic control problems. The new…
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state space, providing a more natural approach for modeling…
This work addresses the inverse problem of espresso coffee extraction, in which one aims to reconstruct the brewing conditions that generate a desired chemical profile in the final beverage. Starting from a high-fidelity multiphysics…