Zamana bağımlı bir top içindeki Dallanan Brown Hareketi

In this thesis, we study a d-dimensional branching Brownian motion (BBM) evolving inside a subdiffusively expanding ball. BBM is a randomly branching stochastic mathematical model where each particle moves under Brownian motion independently of each other. In this model, the particles of BBM are deactivated instantly upon touching the boundary of an expanding ball, but they will be reactivated at a later time provided their ancestral lines are fully inside the expanding ball at that later time. The main quantity of interest is the large-time mass of the BBM inside this time-dependent restricted domain. The study aims at obtaining sharp asymptotic results as time tends to infinity on the large-deviation probability that the mass inside the expanding ball is atypically small. A phase transition is identified concerning the optimal strategies to realize the aforementioned large-deviation event.