Statistical inference of subcritical strongly stationary Galton–Watson processes with regularly varying immigration
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In this article, the authors describe the asymptotic behavior of the conditional least squares estimator of the offspring mean for subcritical strongly stationary Galton-Watson processes with regularly varying immigration with tail index α ∈ ( 1, 2 ).About:
This article is published in Stochastic Processes and their Applications.The article was published on 2021-02-01 and is currently open access. It has received 6 citations till now. The article focuses on the topics: Estimator & Point process.read more
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Lévy processes and infinitely divisible distributions
TL;DR: In this paper, the authors consider the distributional properties of Levy processes and propose a potential theory for Levy processes, which is based on the Wiener-Hopf factorization.
Journal ArticleDOI
Convergence of Probability Measures. By Patrick Billingsley. Pp. xii, 253. 117s. 1968. (John Wiley & Sons, Inc.)
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Convergence of partial sum processes to stable processes with application for aggregation of branching processes
TL;DR: In this paper, a generalization of Theorem 1 in Bartkiewicz, Jakubowski, Mikosch and Wintenberger (2011) is presented, where sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a strongly stationary sequence to a non-Gaussian stable process are given.
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On simultaneous limits for aggregation of stationary randomized INAR(1) processes with Poisson innovations
TL;DR: In this article, the authors investigated joint temporal and contemporaneous aggregation of N independent copies of strictly stationary INteger-valued AutoRegressive processes of order 1 (INAR(1)) with random coefficient $\alpha\in(0,1)$ and with idiosyncratic Poisson innovations.
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Convergence of partial sum processes to stable processes with application for aggregation of branching processes
TL;DR: In this paper , the authors give sufficient conditions for weak convergence of finite dimensional distributions of the partial sum processes of a strongly stationary sequence to the corresponding finite-dimensional distributions of a non-Gaussian stable process instead of weak convergences of partial sums themselves to a nonGaussian standing process.
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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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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Extreme Values, Regular Variation, and Point Processes
TL;DR: In this paper, the authors present a survey of the main domains of attraction and norming constants in point processes and point processes, and their relationship with multivariate extremity processes.
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Stable Non-Gaussian Random Processes : Stochastic Models with Infinite Variance
TL;DR: In this paper, the authors introduce sample path properties such as boundedness, continuity, and oscillations, as well as integrability, and absolute continuity of the path in the real line.
Related Papers (5)
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