Functional convergence for moving averages with heavy tails and random coefficients
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In this article, the authors studied functional convergence of sums of moving averages with random coefficients and heavy-tailed innovations under some standard moment conditions and the assumption that all partial sums of the series of coefficients are a.s.Abstract:
We study functional convergence of sums of moving averages with random coefficients and heavy-tailed innovations. Under some standard moment conditions and the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series we obtain functional convergence of the corresponding partial sum stochastic process in the space $D[0,1]$ of cadlag functions with the Skorohod $M_{2}$ topology.read more
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Journal ArticleDOI
Convergence of Probability Measures. By Patrick Billingsley. Pp. xii, 253. 117s. 1968. (John Wiley & Sons, Inc.)
Journal ArticleDOI
Maxima Of Linear Processes With Heavy-Tailed Innovations And Random Coefficients
TL;DR: In this paper, the authors derive functional convergence of the partial maxima stochastic process in the space of cadlag functions on $[0,1]$ with the Skorohod $M_{1}$ topology.
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A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations
TL;DR: The functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the coefficients as discussed by the authors.
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Maxima of linear processes with heavy-tailed innovations and random coefficients
TL;DR: In this paper, the authors derive functional convergence of the partial maxima stochastic process in the space of cadlag functions on $[0,1]$ with the Skorohod $M_{1}$ topology.
Journal ArticleDOI
A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations
TL;DR: The functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the coefficients as mentioned in this paper .
References
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Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
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Jean Jacod,Albert N. Shiryaev +1 more
TL;DR: In this article, the General Theory of Stochastic Processes, Semimartingales, and Stochastically Integrals is discussed and the convergence of Processes with Independent Increments is discussed.
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TL;DR: In this paper, a comprehensive introduction to probability theory covering laws of large numbers, central limit theorem, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion is presented.
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Foundations of modern probability
TL;DR: In this article, the authors discuss the relationship between Markov Processes and Ergodic properties of Markov processes and their relation with PDEs and potential theory. But their main focus is on the convergence of random processes, measures, and sets.
Journal ArticleDOI
Association of Random Variables, with Applications
TL;DR: In this paper, it was shown that a random variable can be associated with another random variable if the test functions are either (a) binary or (b) bounded and continuous.
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