We consider a particle system in continuous time, a discrete population, with spatial motion, and nonlocal branching. The offspring's positions and their number may depend on the mother's position.

Let $X_{t},\ t\dot{\in }Z^{m}$, be a Markov random field assuming values in RM. Let In be a rectangular box in Zm with its center at 0 and corner points with ...

Random fields provide a versatile mathematical framework to describe spatially dependent phenomena, ranging from physical systems and quantum chaos to cosmology and spatial statistics. Underpinning ...

Random walks constitute one of the cornerstone concepts in probability theory and statistical physics, representing a class of stochastic processes in which a moving entity takes successive steps in ...