49 citations · 157 across the 34 of their papers we have counts for
41 papers
Markov processes forced on a subspace by a large drift, with applications to population genetics
Samuel Ayomide Adeosun, Peter Pfaffelhuber
Consider a sequence of Markov processes with state space , where has a strong drift to , such that is slow for some appropriate $Φ:…
A diploid population model for copy number variation of genetic elements
Peter Pfaffelhuber, Anton Wakolbinger
We study the following model for a diploid population of constant size : Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the tw…
A unified framework for limit results in Chemical Reaction Networks on multiple time-scales
Timo Enger, Peter Pfaffelhuber
If is a sequence of Markov processes which solve the martingale problems for some operators , it is a classical task to derive a limit result…
A central limit theorem concerning uncertainty in estimates of individual admixture
Peter Pfaffelhuber, Angelika Rohde
The concept of individual admixture (IA) assumes that the genome of individuals is composed of alleles inherited from ancestral populations. Each copy of each allele has the sa…
The Martingale Problem Method Revisited
David Criens, Peter Pfaffelhuber, Thorsten Schmidt
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is n…
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 on the complete graph with nodes. Each vertex is either excitatory (probability ) or inhibitory (probability ).…