Stochastic processes provide a rigorous framework for modelling systems that evolve over time under uncertainty, while extremal theory offers the tools for understanding the behaviour of rare, ...

Hilbert spaces provide a fundamental mathematical framework for analysing infinite-dimensional vector spaces endowed with an inner product. In the context of stochastic processes, these spaces serve ...

A cylindrical Lévy process does not enjoy a cylindrical version of the semimartingale decomposition which results in the need to develop a completely novel approach to stochastic integration. In this ...

Editor's note: As the following article is a chapter (Chapter 8) from David Koenig's book, Practical Control Engineering: Guide for Engineers, Managers, and Practitioners (MATLAB Examples) (McGraw ...

Brazilian Journal of Probability and Statistics, Vol. 34, No. 3 (2020), pp. 658-684 (27 pages) The existence of an invariant probability measure is proven for a class of solutions of stochastic ...

This course provides doctoral students the foundations of applied probability and stochastic modeling. The first part of the course covers basic concepts in probability, such as the Borel Cantelli ...

Simulation research derives new methods for the design, analysis, and optimization of simulation experiments. Research on stochastic models develops and analyzes models of systems with random behavior ...

As global financial markets become increasingly interconnected, accurately modelling correlations between assets is essential. Traditional models often assume static correlations, which fail to ...

Several vendors are rolling out next-generation inspection systems and software that locates problematic defects in chips caused by processes in extreme ultraviolet (EUV) lithography. Each defect ...