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, ...

Affine processes provide a versatile framework for modelling complex financial phenomena, ranging from interest rate dynamics to credit risk and beyond. Their defining characteristic is the affine, or ...

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

The paper investigates stochastic processes directed by a randomized time process. A new family of directing processes called Hougaard processes is introduced. Monotonicity properties preserved under ...

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 ...

In extreme ultraviolet (EUV) lithography, stochastics are events that have random variables. These variations, called stochastic effects, sometimes cause unwanted defects and pattern roughness in ...

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 ...