A Central Limit Theorem for General Stochastic Processes
نویسندگان
چکیده
منابع مشابه
On the Central Limit Theorem for Multiparameter Stochastic Processes
l.INTRODUCTION AND RESULTS In recent papers Bezandry and Fernique (1990,1992), Fernique (1993) have given new convergence and tightness criteria for random processes whose sample paths are right-continuous and have leftlimits. These criteria have been applied by Bezandry and Fernique, Bloznelis and Paulauskas to prove the central limit theorem (CLT) in the Skorohod space D[0, 1]. In this paper,...
متن کاملCentral 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.
متن کاملCentral 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 کاملA Central Limit Theorem for Fluctuations in 1d Stochastic Homogenization
In this paper, we analyze the random fluctuations in a 1D stochastic homogenization problem and prove a central limit theorem: the first order fluctuations is described by a Gaussian process that solves an SPDE with an additive spatial white noise. Using a probabilistic approach, we obtain a precise error decomposition up to the first order, which also helps to decompose the limiting Gaussian p...
متن کاملNon-central limit theorem for the cubic variation of a class of selfsimilar stochastic processes
By using multiple Wiener-Itô stochastic integrals, we study the cubic variation of a class of selfsimilar stochastic processes with stationary increments (the Rosenblatt process with selfsimilarity order H ∈ ( 12 , 1)). This study is motivated by statistical purposes. We prove that this renormalized cubic variation satis es a non-central limit theorem and its limit is (in the L(Ω) sense) still ...
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: Canadian Mathematical Bulletin
سال: 1979
ISSN: 0008-4395,1496-4287
DOI: 10.4153/cmb-1979-016-0