Sebastian Mentemeier

activity

20182025

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Showing math.PRShow all

6 papers · 1 filter

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 stochastic exponentials of matrix-valued Lévy processes

Anita Behme, Sebastian Mentemeier

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

math.PR2023

Limit theorems for first passage times of multivariate perpetuity sequences

Sebastian Mentemeier, Hui Xiao

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

math.PR2018

Absolute Continuity of Complex Martingales and of Solutions to Complex Smoothing Equations

Ewa Damek, Sebastian Mentemeier

Let $X$ be a $C$ -valued random variable with the property that $X has the same law as j \geq 1 \sum T_{j} X_{j}$ where $X_{j}$ are i.i.d.\ copies of $X$ , which are…