A critical branching process {Zk, k = 0, 1, 2,...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established ...

Random walks constitute a foundational concept in probability theory, describing the seemingly erratic movement of particles or agents as they traverse a space in a series of stochastic steps. In many ...

Tiny particles like pollen grains move constantly, pushed and pulled by environmental forces. To study this motion, physicists use a “random walk” model — a system in which every step is determined by ...

Branching processes in random environments constitute a significant class of stochastic models designed to capture the interplay between intrinsic reproductive dynamics and extrinsic environmental ...