منابع مشابه
Central Limit Theorem for Stationary Linear Processes
We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. In doing so we shall preserve the generality of the coefficients, including the long range dependence case, and we shall express the variance of partial sums in a form easy to apply. Ergodicity is not required.
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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...
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A Poisson process in space{time is used to generate a linear Kolmogorov's birth{growth model. Points start to form on 0; L] at time zero. Each newly formed point initiates two bidirectional moving frontiers of constant speed. New points continue to form on not-yet passed over parts of 0; L]. The whole interval will eventually be passed over by moving frontiers. Let N L be the total number of po...
متن کاملLocal Central Limit Theorem for Determinantal Point Processes
We prove a local central limit theorem (LCLT) for the number of points N(J) in a region J in Rd specified by a determinantal point process with an Hermitian kernel. The only assumption is that the variance of N(J) tends to infinity as |J | → ∞. This extends a previous result giving a weaker central limit theorem (CLT) for these systems. Our result relies on the fact that the Lee-Yang zeros of t...
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On any aperiodic measure preserving system, there exists a square integrable function such that the associated stationary process satifies the Almost Sure Central Limit Theorem. Introduction The Almost Sure Central Limit Theorem (ASCLT), first formulated by Lévy in [9], has been studied by various authors at the end of the eighties ([6], [3], [10], [8]). This theorem gives conditions under whic...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1997
ISSN: 0091-1798
DOI: 10.1214/aop/1024404295