Particle systems with a singular mean-field self-excitation. Application to neuronal networks
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DOI: 10.1016/j.spa.2015.01.007
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References listed on IDEAS
- Ward Whitt, 2001. "The Reflection Map with Discontinuities," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 447-484, August.
- Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
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Cited by:
- Erhan Bayraktar & Gaoyue Guo & Wenpin Tang & Yuming Paul Zhang, 2022. "Systemic robustness: a mean-field particle system approach," Papers 2212.08518, arXiv.org, revised Aug 2023.
- Cormier, Quentin & Tanré, Etienne & Veltz, Romain, 2020. "Long time behavior of a mean-field model of interacting neurons," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 2553-2595.
- Chevallier, Julien, 2017. "Mean-field limit of generalized Hawkes processes," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3870-3912.
- Sean Ledger & Andreas Sojmark, 2018. "Uniqueness for contagious McKean--Vlasov systems in the weak feedback regime," Papers 1811.12356, arXiv.org, revised Oct 2019.
- Christa Cuchiero & Christoph Reisinger & Stefan Rigger, 2024. "Optimal bailout strategies resulting from the drift controlled supercooled Stefan problem," Annals of Operations Research, Springer, vol. 336(1), pages 1315-1349, May.
- Kumar, Santosh & Singh, Paramjeet, 2019. "High order WENO finite volume approximation for population density neuron model," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 173-189.
- Roman Gayduk & Sergey Nadtochiy, 2020. "Control-Stopping Games for Market Microstructure and Beyond," Mathematics of Operations Research, INFORMS, vol. 45(4), pages 1289-1317, November.
- Ben Hambly & Andreas Sojmark, 2018. "An SPDE Model for Systemic Risk with Endogenous Contagion," Papers 1801.10088, arXiv.org, revised Sep 2018.
- Sirignano, Justin & Spiliopoulos, Konstantinos, 2020. "Mean field analysis of neural networks: A central limit theorem," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1820-1852.
- Ben Hambly & Andreas Søjmark, 2019. "An SPDE model for systemic risk with endogenous contagion," Finance and Stochastics, Springer, vol. 23(3), pages 535-594, July.
- Erhan Bayraktar & Gaoyue Guo & Wenpin Tang & Yuming Zhang, 2020. "McKean-Vlasov equations involving hitting times: blow-ups and global solvability," Papers 2010.14646, arXiv.org, revised Jul 2023.
- Sean Ledger & Andreas Sojmark, 2018. "At the Mercy of the Common Noise: Blow-ups in a Conditional McKean--Vlasov Problem," Papers 1807.05126, arXiv.org, revised Mar 2024.
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More about this item
Keywords
McKean nonlinear diffusion process; Counting process; Propagation of chaos; Integrate-and-fire network; Skorohod M1 topology; Neuroscience;All these keywords.
JEL classification:
- M1 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration
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