Sebastian Mentemeier

collaborators

6 papers

math.PR2025

Hidden regular variation for stochastic recursions with diagonal matrices

Ewa Damek, Sebastian Mentemeier

We consider random vectors $X$ that satisfy the equation in law $X = A X + B$ , where $A$ is a given random diagonal matrix and $B$ a given random vector, both independent of $X$ . It is…

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…

math.PR2025

A probabilistic study of the set of stationary solutions to spatial kinetic-type equations

Sebastian Mentemeier, Glib Verovkin

In this paper we study multivariate kinetic-type equations in a general setup, which includes in particular the spatially homogeneous Boltzmann equation with Maxwellian molecules,…

math.PR2024

Limit theorems for first passage times of multivariate perpetuity sequences

Sebastian Mentemeier, Hui Xiao

We study the first passage time $I ¨ _{u} = in f {n \geq 1 : ∣ V_{n} ∣ > u}$ for the multivariate perpetuity sequence $V_{n} = Q_{1} + M_{1} Q_{2} + \dots + (M_{1} \dots M_{n - 1}) Q_{n}$ , where $(…

math.PR2024

The extremal position of a branching random walk on the general linear group

Ion Grama, Sebastian Mentemeier, Hui Xiao

Consider a branching random walk $(G_{u})_{u \in T}$ on the general linear group $GL (V)$ of a finite dimensional space $V$ , where $T$ is the associated geneal…

math.PR2024

Anita Behme, Sebastian Mentemeier

We study the long-time behaviour of matrix-valued stochastic exponentials of LÃ©vy processes, i.e. of multiplicative LÃ©vy processes in the general linear group. In particular, we…

Hidden regular variation for stochastic recursions with diagonal matrices

Spinal decomposition, martingale convergence and the Seneta-Heyde scaling for matrix branching random walks

A probabilistic study of the set of stationary solutions to spatial kinetic-type equations

Limit theorems for first passage times of multivariate perpetuity sequences

The extremal position of a branching random walk on the general linear group

Limit theorems for stochastic exponentials of matrix-valued LÃ©vy processes