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Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds
To recover the topology of a manifold in the presence of heavy tailed or exponentially decaying noise, one must understand the behavior of geometric...
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A Limit Theorem for Fluctuations
To motivate the results of this chapter, consider the classical strong law of large numbers: Let...
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Specification procedures for multivariate stable-Paretian laws for independent and for conditionally heteroskedastic data
We consider goodness-of-fit methods for multivariate symmetric and asymmetric stable Paretian random vectors in arbitrary dimension. The methods are...
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Strong Consistency for the Conditional Self-weighted M Estimator of GRCA(p) Models
In this paper, we investigate the strong consistency for the conditional self-weighted M ( SM , for short) estimator of generalized random coefficient...
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Structural properties of generalised Planck distributions
A family of generalised Planck (GP) laws is defined and its structural properties explored. Sometimes subject to parameter restrictions, a GP law is...
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Profile of Random Exponential Recursive Trees
We introduce the random exponential recursive tree in which at each point of discrete time every node recruits a child (new leaf) with probability p ,...
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Fast simulation of tempered stable Ornstein–Uhlenbeck processes
Constructing Lévy-driven Ornstein–Uhlenbeck processes is a task closely related to the notion of self-decomposability. In particular, their...
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Uniform Strong Law of Large Numbers
We prove the strong law of large numbers for random signed measures. The result is uniform over a family of subsets under mild assumptions.
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Testing Poissonity of a large number of populations
This paper studies the problem of simultaneously testing that each of k samples, coming from k count variables, were all generated by Poisson laws....
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Convergence of Random Variables
In this chapter, we discuss sequences of random variables and their convergence. The central limit theorem, one of the most important and widely-used...
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On the Baum–Katz theorem for randomly weighted sums of negatively associated random variables with general normalizing sequences and applications in some random design regression models
In this paper, we develop Jajte’s technique, which is used in the proof of strong laws of large numbers, to prove complete convergence for randomly...
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Parametric and non-parametric estimation of extreme earthquake event: the joint tail inference for mainshocks and aftershocks
In an earthquake event, the combination of a strong mainshock and damaging aftershocks is often the cause of severe structural damages and/or high...
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Nonlinear Unbalanced Urn Models via Stochastic Approximation
This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our...
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Exchangeable min-id sequences: Characterization, exponent measures and non-decreasing id-processes
We establish a one-to-one correspondence between (i) exchangeable sequences of random variables whose finite-dimensional distributions are minimum...
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On the Asymptotic Behaviour of Extremes of Observations from a Tempered Stable Distribution
In this article, we obtain the limit distribution of the maxima and minima of independent observations from tempered stable and bilateral gamma...
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Central Limit Theorems for Conditional Empirical and Conditional U-Processes of Stationary Mixing Sequences
In this paper we are concerned with the weak convergence to Gaussian processes of conditional empirical processes and conditional U -processes from...
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Mixing convergence of LSE for supercritical AR(2) processes with Gaussian innovations using random scaling
We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with...
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Targeting Sedentary Behaviour at the Policy Level
Policy-level approaches are a promising and potentially powerful way to reduce sedentary behaviour at a population level. Ecological models have...
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Laws of Large Numbers for Non-Homogeneous Markov Systems
In the present we establish Laws of Large Numbers for Non-Homogeneous Markov Systems and Cyclic Non-homogeneous Markov systems. We start with a...