Renewal in Hawkes processes with self-excitation and inhibition
نویسندگان
چکیده
منابع مشابه
Hawkes processes in finance
In this paper we propose an overview of the recent academic literature devoted to the applications of Hawkes processes in finance. Hawkes processes constitute a particular class of multivariate point processes that has become very popular in empirical high frequency finance this last decade. After a reminder of the main definitions and properties that characterize Hawkes processes, we review th...
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0 g⇤(w⇤ ·xt)dt = P j2Si aijg ⇤ (w⇤ ·xj). Set y⇤ i = g ⇤ (w⇤ ·xi) to be the expected value of each yi. Let ̄ Ni be the expected value of Ni. Then we have ̄ Ni = P j2Si aijy ⇤ j . Clearly we do not have access to ̄ Ni. However, consider a hypothetical call to the algorithm with input {(xi, ̄ Ni)}i=1 and suppose it returns ḡk. In this case, we define ȳk i = ḡk(w̄k · xi). Next we begin the proof and int...
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Hawkes processes are powerful tools for modeling the mutual-excitation phenomena commonly observed in event data from a variety of domains, such as social networks, quantitative finance and healthcare records. The intensity function of a Hawkes process is typically assumed to be linear in the sum of triggering kernels, rendering it inadequate to capture nonlinear effects present in real-world d...
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ژورنال
عنوان ژورنال: Advances in Applied Probability
سال: 2020
ISSN: 0001-8678,1475-6064
DOI: 10.1017/apr.2020.19