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On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

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Název: On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications
Autoři: Hongler, Max-Olivier, Filliger, Roger
Informace o vydavateli: Springer
Dordrecht
Rok vydání: 2017
Sbírka: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
Témata: Markov jump-diffusive processes - Meanfield approach to multi-agents systems - Flocking beahvior of swarms
Popis: We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial differential equation without integral term. This differential form is valid for statedependent Poisson rates and we use it to characterize, via a mean-field approach, the collective dynamics of a large population of pure jump processes interacting via their Poisson rates. We explicitly show that for an appropriate class of interactions, the speed of a tight collective traveling wave behavior can be triggered by the jump size parameter m. As a second application we consider an exceptional class of stochastic differential equations with nonlinear drift, Poisson shot noise and an additional White Gaussian Noise term, for which explicit solutions to the associated Master equation are derived. ; STI
Druh dokumentu: article in journal/newspaper
Jazyk: unknown
Relation: https://infoscience.epfl.ch/record/227404/files/HON_FILL_2017.pdf; Methodoly and Computing in Applied Probability; https://infoscience.epfl.ch/handle/20.500.14299/136480; WOS:000484932800007
DOI: 10.1007/s11009-017-9566-3
Dostupnost: https://doi.org/10.1007/s11009-017-9566-3
https://infoscience.epfl.ch/handle/20.500.14299/136480
https://hdl.handle.net/20.500.14299/136480
Přístupové číslo: edsbas.A69A2643
Databáze: BASE
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  – Url: https://doi.org/10.1007/s11009-017-9566-3#
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  Data: On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications
– Name: Author
  Label: Authors
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  Data: <searchLink fieldCode="AR" term="%22Hongler%2C+Max-Olivier%22">Hongler, Max-Olivier</searchLink><br /><searchLink fieldCode="AR" term="%22Filliger%2C+Roger%22">Filliger, Roger</searchLink>
– Name: Publisher
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  Data: Springer<br />Dordrecht
– Name: DatePubCY
  Label: Publication Year
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  Data: 2017
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  Data: Ecole Polytechnique Fédérale Lausanne (EPFL): Infoscience
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  Data: <searchLink fieldCode="DE" term="%22Markov+jump-diffusive+processes+-+Meanfield+approach+to+multi-agents+systems+-+Flocking+beahvior+of+swarms%22">Markov jump-diffusive processes - Meanfield approach to multi-agents systems - Flocking beahvior of swarms</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial differential equation without integral term. This differential form is valid for statedependent Poisson rates and we use it to characterize, via a mean-field approach, the collective dynamics of a large population of pure jump processes interacting via their Poisson rates. We explicitly show that for an appropriate class of interactions, the speed of a tight collective traveling wave behavior can be triggered by the jump size parameter m. As a second application we consider an exceptional class of stochastic differential equations with nonlinear drift, Poisson shot noise and an additional White Gaussian Noise term, for which explicit solutions to the associated Master equation are derived. ; STI
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  Data: article in journal/newspaper
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  Data: https://infoscience.epfl.ch/record/227404/files/HON_FILL_2017.pdf; Methodoly and Computing in Applied Probability; https://infoscience.epfl.ch/handle/20.500.14299/136480; WOS:000484932800007
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  Data: 10.1007/s11009-017-9566-3
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  Data: https://doi.org/10.1007/s11009-017-9566-3<br />https://infoscience.epfl.ch/handle/20.500.14299/136480<br />https://hdl.handle.net/20.500.14299/136480
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      – SubjectFull: Markov jump-diffusive processes - Meanfield approach to multi-agents systems - Flocking beahvior of swarms
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      – TitleFull: On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications
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