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Central Limit Theorems
In the previous chapter, we have studied some random variables which come up naturally when a stationary Poisson hyperplane process is observed...
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Multivariate central limit theorems for random clique complexes
Motivated by open problems in applied and computational algebraic topology, we establish multivariate normal approximation theorems for three random...
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Central limit theorems for random multiplicative functions
A Steinhaus random multiplicative function f is a completely multiplicative function obtained by setting its values on primes f ( p ) to be independent...
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Central limit theorems for nonlinear stochastic wave equations in dimension three
In this paper, we consider three-dimensional nonlinear stochastic wave equations driven by the Gaussian noise which is white in time and has some...
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Stable Central Limit Theorems for Super Ornstein-Uhlenbeck Processes, II
This paper is a continuation of our recent paper ( Electron. J. Probab. , 24 (141), (2019)) and is devoted to the asymptotic behavior of a class of...
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Functional Shige Peng’s Central Limit Theorems for Martingale Vectors
In this paper, the functional central limit theorem is established for martingale like random vectors under the framework sub-linear expectations...
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Functional central limit theorems for rough volatility
The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate...
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Strong Limit Theorems for Weighted Sums under the Sub-linear Expectations
In this article, we study strong limit theorems for weighted sums of extended negatively dependent random variables under the sub-linear...
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Almost sure central limit theorems for the maxima of randomly chosen random variables
In this paper, we give an almost sure central limit theorem (ASCLT) version of a maximum limit theorem (MLT) with an arbitrary sequence { d n , n ≥ 1}...
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High-Dimensional Central Limit Theorems for Homogeneous Sums
This paper develops a quantitative version of de Jong’s central limit theorem for homogeneous sums in a high-dimensional setting. More precisely,...
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Local Limit Theorems for Inhomogeneous Markov Chains
This book extends the local central limit theorem to Markov chains whose state spaces and transition probabilities are allowed to change in time....
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Asymptotic Expansions and Two-Sided Bounds in Randomized Central Limit Theorems
Lower and upper bounds are explored for the uniform (Kolmogorov) and...
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A Note on Central Limit Theorems for Trimmed Subordinated Subordinators
In this note, we prove self-standardized central limit theorems (CLTs) for trimmed subordinated subordinators. We shall see that there are two ways...
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Limit Theorems for Random Sums of Random Summands
We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner-growth...
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On Limit Theorems for Functional Autoregressive Processes with Random Coefficients
AbstractIn this paper we consider a Banach space valued random coefficient autoregressive process. Our studies on this process involve existence,...
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Limit Theorems for Deviation Means of Independent and Identically Distributed Random Variables
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called...
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Limit theorems of Brownian additive functionals
We reconfirm some classical results that the local time process is a proper scale to find limits of additive functionals of Brownian motion [
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Precise Asymptotics in Limit Theorems for a Supercritical Branching Process with Immigration in a Random Environment
Let ( Z n ) be a supercritical branching process with immigration in an independent and identically distributed random environment. Under necessary...
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Central limit theorems for the ℤ2-periodic Lorentz gas
This paper is devoted to the stochastic properties of dynamical systems preserving an infinite measure. More precisely we prove central limit...