Jakob Stiefel

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20192022

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math.PR2022

Mean-field limits for non-linear Hawkes processes with inhibition on a Erdős-Rényi-graph

Jakob Stiefel

We study a multivariate, non-linear Hawkes process $Z^{N}$ on a $q$ -Erdős-Rényi-graph with $N$ nodes. Each vertex is either excitatory (probability $p$ ) or inhibitory (probability $1…

math.PR2021

Mean-field limits for non-linear Hawkes processes with excitation and inhibition

Peter Pfaffelhuber, Stefan Rotter, Jakob Stiefel

We study a multivariate, non-linear Hawkes process $Z^{N}$ on the complete graph with $N$ nodes. Each vertex is either excitatory (probability $p$ ) or inhibitory (probability $1 - p$ ).…

math.PR2019

The range of once-reinforced random walk in one dimension

Peter Pfaffelhuber, Jakob Stiefel

We study once-reinforced random walk (ORRW) on $Z$ . For this model, we derive limit results on all moments of its range using Tauberian theory.