Approximate Simulation of Hawkes Processes
نویسندگان
چکیده
منابع مشابه
Approximate Simulation of Hawkes Processes
This article concerns a simulation algorithm for unmarked and marked Hawkes processes. The algorithm suffers from edge effects but is much faster than the perfect simulation algorithm introduced in our previous work [12]. We derive various useful measures for the error committed when using the algorithm, and we discuss various empirical results for the algorithm compared with perfect simulations.
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Hawkes processes are a particularly interesting class of stochastic processes that were introduced in the early seventies by A. G. Hawkes, notably to model the occurrence of seismic events. Since then they have been applied in diverse areas, from earthquake modeling to financial analysis. The processes themselves are characterized by a stochastic intensity vector, which represents the condition...
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Motivated by the availability of continuous event sequences that trace the social behavior in a population e.g. email, we believe that mutually exciting Hawkes processes provide a realistic and informative model for these sequences. For complex mutually exciting processes, the numerical optimization used for univariate self exciting processes may not provide stable estimates. Furthermore, conve...
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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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ژورنال
عنوان ژورنال: Methodology and Computing in Applied Probability
سال: 2006
ISSN: 1387-5841,1573-7713
DOI: 10.1007/s11009-006-7288-z