Mean-field limits for non-linear Hawkes processes with excitation and inhibition
نویسندگان
چکیده
We study a multivariate, non-linear Hawkes process ZN on the complete graph with N nodes. Each vertex is either excitatory (probability p) or inhibitory 1?p). take mean-field limit of ZN, leading to multivariate point Z?. If p?12, we rescale interaction intensity by and find that solves deterministic convolution equation all components Z? are independent. In critical case, p=12, N1/2 obtain intensity, which stochastic conditionally
منابع مشابه
Mean-field inference of Hawkes point processes
We propose a fast and efficient estimation method that is able to accurately recover the parameters of a d-dimensional Hawkes point-process from a set of observations. We exploit a mean-field approximation that is valid when the fluctuations of the stochastic intensity are small. We show that this is notably the case in situations when interactions are sufficiently weak, when the dimension of t...
متن کاملFluctuations for mean-field interacting age-dependent Hawkes processes
The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +∞) being granted by the study performed in [9], the aim of the present paper is to prove the resulting functional central limit theorem. It involves the study of a measure-valued process describing the fluctuations (at scale n) of the em...
متن کاملScaling limits for Hawkes processes and application to financial statistics
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval [0, T ] in the limit T → ∞. We further exhibit the asymptotic behaviour of the covariation of the increments of the components of a multivariate Hawkes process, when the observations are imposed by a discrete scheme with mesh ∆ over [0, T ] up to some further ti...
متن کاملchaotic motion and its control for a non-planar non-linear cantilever beam with parametric excitation
in this paper, chaotic motion analysis and its control for a non-planar non-linear cantilever beam with axial and lateral parametric excitation in the free end is accomplished. this is a new method for control of chaotic motion of a non-linear planar beam. in this survey, internal resonance of the beam is 2:1 and the initial resonance is in the outside of plane and it is assumed a sub-resonance...
متن کاملa new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot
abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 2022
ISSN: ['1879-209X', '0304-4149']
DOI: https://doi.org/10.1016/j.spa.2022.07.006