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math.PR2025
Local limit theorems for conditioned random walks by the heat kernel approximation
Ion Grama, Hui Xiao
We study the random walk with independent and identically distributed real-valued increments having zero mean and an absolute moment of order for some $δ>…
math.PR2025
Spinal decomposition, martingale convergence and the Seneta-Heyde scaling for matrix branching random walks
Ion Grama, Sebastian Mentemeier, Hui Xiao
We consider a matrix branching random walk on the semi-group of nonnegative matrices, where we are able to derive, under general assumptions, an analogue of Biggins' martingale con…