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

[1]  W. Stannat,et al.  Fluctuation limits for mean-field interacting nonlinear Hawkes processes , 2019, 1912.10854.

[2]  Julien Chevallier,et al.  Fluctuations for spatially extended Hawkes processes , 2019, Stochastic Processes and their Applications.

[3]  Kenneth D. Miller,et al.  What is the dynamical regime of cerebral cortex? , 2019, Neuron.

[4]  Eva Locherbach,et al.  Mean field limits for interacting Hawkes processes in a diffusive regime , 2019, Bernoulli.

[5]  A. Hawkes.  Hawkes processes and their applications to finance: a review , 2018 .

[6]  Manon Costa,et al.  Renewal in Hawkes processes with self-excitation and inhibition , 2018, Advances in Applied Probability.

[7]  P. D. Pra,et al.  Stochastic Mean-Field Dynamics and Applications to Life Sciences , 2017 .

[8]  G. Ost,et al.  Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels , 2017, Stochastic Processes and their Applications.

[9]  Felipe Gerhard,et al.  On the stability and dynamics of stochastic spiking neuron models: Nonlinear Hawkes process and point process GLMs , 2017, PLoS Comput. Biol..

[10]  Julien Chevallier.  Fluctuations for mean-field interacting age-dependent Hawkes processes , 2016, 1611.02008.

[11]  J. Barral,et al.  Synaptic scaling rule preserves excitatory–inhibitory balance and salient neuronal network dynamics , 2016, Nature Neuroscience.

[12]  Eric Warren Fox,et al.  Spatially inhomogeneous background rate estimators and uncertainty quantification for nonparametric Hawkes point process models of earthquake occurrences , 2016 .

[13]  Arkaitz Zubiaga,et al.  Hawkes Processes for Continuous Time Sequence Classification: an Application to Rumour Stance Classification in Twitter , 2016, ACL.

[14]  S. Delattre,et al.  HAWKES PROCESSES ON LARGE NETWORKS , 2016 .

[15]  E. Locherbach,et al.  Multi-class oscillating systems of interacting neurons , 2015, 1512.00265.

[16]  Julien Chevallier.  Mean-field limit of generalized Hawkes processes , 2015, 1510.05620.

[17]  Andrea L. Bertozzi,et al.  Point-process models of social network interactions: Parameter estimation and missing data recovery , 2015, European Journal of Applied Mathematics.

[18]  E. Bacry,et al.  Hawkes Processes in Finance , 2015, 1502.04592.

[19]  Stefan Rotter,et al.  Cumulants of Hawkes point processes. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Lingjiong Zhu,et al.  Central Limit Theorem for Nonlinear Hawkes Processes , 2012, Journal of Applied Probability.

[21]  Lief E. Fenno,et al.  Neocortical excitation/inhibition balance in information processing and social dysfunction , 2011, Nature.

[22]  Lingjiong Zhu,et al.  Large deviations for Markovian nonlinear Hawkes processes , 2011, 1108.2432.

[23]  Stefan Rotter,et al.  How Structure Determines Correlations in Neuronal Networks , 2011, PLoS Comput. Biol..

[24]  S. Herculano‐Houzel.  The Human Brain in Numbers: A Linearly Scaled-up Primate Brain , 2009, Front. Hum. Neurosci..

[25]  Tim Gollisch,et al.  Modeling Single-Neuron Dynamics and Computations: A Balance of Detail and Abstraction , 2006, Science.

[26]  Eero P. Simoncelli,et al.  Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model , 2004, Neural Computation.

[27]  Nicolas Brunel,et al.  Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons , 2000, Journal of Computational Neuroscience.

[28]  Haim Sompolinsky,et al.  Chaotic Balanced State in a Model of Cortical Circuits , 1998, Neural Computation.

[29]  Laurent Massoulié,et al.  Stability results for a general class of interacting point processes dynamics, and applications , 1998 .

[30]  P. Brémaud,et al.  STABILITY OF NONLINEAR HAWKES PROCESSES , 1996 .

[31]  Yosihiko Ogata,et al.  Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes , 1988 .

[32]  A. Hawkes,et al.  A cluster process representation of a self-exciting process , 1974, Journal of Applied Probability.

[33]  A. Hawkes.  Spectra of some self-exciting and mutually exciting point processes , 1971 .

[34]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[35]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .