Gaussian approximation of nonlinear Hawkes processes
نویسندگان
چکیده
منابع مشابه
Central Limit Theorem for Nonlinear Hawkes Processes
Hawkes process is a self-exciting point process with clustering effect whose jump rate depends on its entire past history. It has wide applications in neuroscience, finance and many other fields. Linear Hawkes process has an immigration-birth representation and can be computed more or less explicitly. It has been extensively studied in the past and the limit theorems are well understood. On the...
متن کاملLarge Deviations for Markovian Nonlinear Hawkes Processes
In the 2007 paper, Bordenave and Torrisi [1] proves the large deviation principles for Poisson cluster processes and in particular, the linear Hawkes processes. In this paper, we prove first a large deviation principle for a special class of nonlinear Hawkes process, i.e. a Markovian Hawkes process with nonlinear rate and exponential exciting function, and then generalize it to get the result f...
متن کاملProper Loss Functions for Nonlinear Hawkes Processes
Temporal point processes are a statistical framework for modelling the times at which events of interest occur. The Hawkes process is a well-studied instance of this framework that captures self-exciting behaviour, wherein the occurrence of one event increases the likelihood of future events. Such processes have been successfully applied to model phenomena ranging from earthquakes to behaviour ...
متن کاملNonlinear Approximation Using Gaussian Kernels
It is well-known that non-linear approximation has an advantage over linear schemes in the sense that it provides comparable approximation rates to those of the linear schemes, but to a larger class of approximands. This was established for spline approximations and for wavelet approximations, and more recently for homogeneous radial basis function (surface spline) approximations. However, no s...
متن کاملProcess-level Large Deviations for Nonlinear Hawkes Point Processes
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.
متن کاملذخیره 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: The Annals of Applied Probability
سال: 2016
ISSN: 1050-5164
DOI: 10.1214/15-aap1141