Stochastic dynamical systems arise in many scientific fields, such as asset prices in financial markets, neural activity in ...

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 ...

The structure of exponential families of stochastic processes with a time-continuous likelihood function is investigated by means of semimartingale theory. The time-homogeneous exponential families of ...

In this paper we consider the second-order real-valued stochastic processes x(t), t ∊ (a, b) ⊂ R, with Ex(t) = 0, for each t, and analyze some characteristic examples of such processes and the ...

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