Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction–diffusion processes are widely used to model such behaviour ...

Stochastic processes provide a mathematical framework to describe systems evolving under intrinsic randomness, while anomalous diffusion refers to the deviation from classical Brownian motion where ...

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 ...

We apply the general theory of stochastic integration to identify a martingale associated with a Lévy process modified by the addition of a secondary process of bounded variation on every finite ...