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Harmonic Analysis of Branching Random Walks with Heavy Tails
We consider a continuous-time symmetric, spatially homogeneous branching random walk on a multidimensional lattice with a single branching source....
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Joint Sum-and-Max Limit for a Class of Long-Range Dependent Processes with Heavy Tails
We consider a class of stationary processes exhibiting both long-range dependence and heavy tails. Separate limit theorems for sums and for extremes...
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Fitting Time Series with Heavy Tails and Strong Time Dependence
Earlier, a model of a time series with heavy tails constructed from a Gaussian time series was developed. In the present paper, the reverse problem...
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On Estimation of the Scale and Location Parameters of Distribution Tails
Estimators of the location and scale parameters are proposed for tails of distributions belonging to the Gumbel or Fréchet maximum domain of...
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Product-Convolution of Heavy-Tailed and Related Distributions
Products of random variables and related distribution problems appear in physics, engineering, number theory, and many probability and statistical...
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On Tests to Distinguish Distribution Tails Invariant with Respect to the Scale Parameter
AbstractWe propose two tests to distinguish between separable classes of distribution tails, the first of which is invariant with respect to the...
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Sample average approximation with heavier tails II: localization in stochastic convex optimization and persistence results for the Lasso
“Localization” has proven to be a valuable tool in the Statistical Learning literature as it allows sharp risk bounds in terms of the problem...
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The Random Conductance Model with Heavy Tails on Nested Fractal Graphs
Recently, Kigami’s resistance form framework has been applied to provide a general approach for deriving the scaling limits of random walks on graphs...
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Algorithms with Gradient Clip** for Stochastic Optimization with Heavy-Tailed Noise
AbstractThis article provides a survey of the results of several research studies [12–14, 26], in which open questions related to the...
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Heavy-Tailed and Related Classes of Distributions
In this chapter, we define the distribution classes whose closure properties will be considered in the subsequent chapters: heavy-tailed...
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Drift estimation for a Lévy-driven Ornstein–Uhlenbeck process with heavy tails
We consider the problem of estimation of the drift parameter of an ergodic Ornstein–Uhlenbeck type process driven by a Lévy process with heavy tails....
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Sample average approximation with heavier tails I: non-asymptotic bounds with weak assumptions and stochastic constraints
We derive new and improved non-asymptotic deviation inequalities for the sample average approximation (SAA) of an optimization problem. Our results...
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Limit behaviors for a heavy-tailed β-mixing random sequence∗
Let { X,X n , n ≥ 1} be a stationary sequence of nonnegative β -mixing random variables with heavy-tailed distributions, and let S n = X 1 + X 2 + · · · + X n ...
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Modeling Right-skewed Heavy-tail Right-censored Survival Data with Application to HIV Viral Load
Right-skewed heavy-tailed survival data commonly arise in health-related studies, and the probability distributions proposed to model such survival...
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One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities
We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic...
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A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations
In this paper, we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and...
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High-Dimensional Volatility Matrix Estimation with Cross-Sectional Dependent and Heavy-Tailed Microstructural Noise
The estimates of the high-dimensional volatility matrix based on high-frequency data play a pivotal role in many financial applications. However,...
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On the number of terms in the COS method for European option pricing
The Fourier-cosine expansion (COS) method is used to price European options numerically in a very efficient way. To apply the COS method, one has to...
