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dc.contributor.authorChevallier, Julien
dc.contributor.authorMelnykova, Anna
dc.contributor.authorTubikanec, Irene
dc.date.accessioned2020-03-30T12:00:04Z
dc.date.available2020-03-30T12:00:04Z
dc.date.issued2020-03-30
dc.identifier.urihttp://publications.mfo.de/handle/mfo/3719
dc.description.abstractOscillatory systems of interacting Hawkes processes with Erlang memory kernels were introduced in Ditlevsen and Löcherbach (2017). They are piecewise deterministic Markov processes (PDMP) and can be approximated by a stochastic diffusion. First, a strong error bound between the PDMP and the diffusion is proved. Second, moment bounds for the resulting diffusion are derived. Third, approximation schemes for the diffusion, based on the numerical splitting approach, are proposed. These schemes are proved to converge with meansquare order 1 and to preserve the properties of the diffusion, in particular the hypoellipticity, the ergodicity and the moment bounds. Finally, the PDMP and the diffusion are compared through numerical experiments, where the PDMP is simulated with an adapted thinning procedure.en_US
dc.language.isoen_USen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2020,09
dc.subjectPiecewise deterministic Markov processesen_US
dc.subjectHawkes processesen_US
dc.subjectStochastic differential equationsen_US
dc.subjectDiffusion processesen_US
dc.subjectNeuronal modelsen_US
dc.subjectNumerical splitting schemesen_US
dc.titleTheoretical Analysis and Simulation Methods for Hawkes Processes and their Diffusion Approximationen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2020-09
local.scientificprogramResearch in Pairs 2020en_US
local.series.idOWP-2020-09en_US
local.subject.msc60en_US
local.subject.msc65en_US


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