A Central Limit Theorem for Extreme Sojourn Times of Stationary Gaussian Processes

1989 ◽  
pp. 81-99
Author(s):  
Simeon M. Berman
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gaussian Processes ◽  
Sojourn Times ◽  
Stationary Gaussian Processes

Central limit theorem for wave-functionals of Gaussian processes

1999 ◽  
Vol 31 (01) ◽  
pp. 158-177 ◽  
Author(s):  
Vladimir Piterbarg ◽  
Igor Rychlik
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gaussian Processes ◽  
Sample Paths

In this paper a central limit theorem is proved for wave-functionals defined as the sums of wave amplitudes observed in sample paths of stationary continuously differentiable Gaussian processes. Examples illustrating this theory are given.

scholarly journals Limit theorems for multivariate Brownian semistationary processes and feasible results

2019 ◽  
Vol 51 (03) ◽  
pp. 667-716
Author(s):  
Riccardo Passeggeri ◽  
Almut E. D. Veraart
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Asymptotic Behaviour ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Laws Of Large Numbers ◽  
Stationary Increments ◽  
Large Numbers ◽  
Weak Laws

AbstractIn this paper we introduce the multivariate Brownian semistationary (BSS) process and study the joint asymptotic behaviour of its realised covariation using in-fill asymptotics. First, we present a central limit theorem for general multivariate Gaussian processes with stationary increments, which are not necessarily semimartingales. Then, we show weak laws of large numbers, central limit theorems, and feasible results for BSS processes. An explicit example based on the so-called gamma kernels is also provided.

scholarly journals Weak Convergence Limits for Sojourn Times in Cyclic Queues Under Heavy Traffic Conditions

2008 ◽  
Vol 45 (2) ◽  
pp. 333-346 ◽  
Author(s):  
Hans Daduna ◽  
Christian Malchin ◽  
Ryszard Szekli
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Weak Convergence ◽  
Central Limit ◽  
Cycle Time ◽  
Heavy Traffic ◽  
Traffic Conditions ◽  
Sojourn Times ◽  
Population Sizes ◽  
Heavy Traffic Conditions

We consider sequences of closed cycles of exponential single-server nodes with a single bottleneck. We study the cycle time and the successive sojourn times of a customer when the population sizes go to infinity. Starting from old results on the mean cycle times under heavy traffic conditions, we prove a central limit theorem for the cycle time distribution. This result is then utilised to prove a weak convergence characteristic of the vector of a customer's successive sojourn times during a cycle for a sequence of networks with population sizes going to infinity. The limiting picture is a composition of a central limit theorem for the bottleneck node and an exponential limit for the unscaled sequences of sojourn times for the nonbottleneck nodes.

scholarly journals Limit theorems for a quadratic variation of Gaussian processes

2011 ◽  
Vol 16 (4) ◽  
pp. 435-452 ◽  
Author(s):  
Raimondas Malukas
Keyword(s):  
Brownian Motion ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Fractional Brownian Motion ◽  
Central Limit ◽  
Gaussian Processes ◽  
Limit Theorems ◽  
Quadratic Variation

In the paper a weighted quadratic variation based on a sequence of partitions for a class of Gaussian processes is considered. Conditions on the sequence of partitions and the process are established for the quadratic variation to converge almost surely and for a central limit theorem to be true. Also applications to bifractional and sub-fractional Brownian motion and the estimation of their parameters are provided.

Central limit theorem for wave-functionals of Gaussian processes

1999 ◽  
Vol 31 (1) ◽  
pp. 158-177 ◽  
Author(s):  
Vladimir Piterbarg ◽  
Igor Rychlik
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gaussian Processes ◽  
Sample Paths

In this paper a central limit theorem is proved for wave-functionals defined as the sums of wave amplitudes observed in sample paths of stationary continuously differentiable Gaussian processes. Examples illustrating this theory are given.

Extensions and Complements

2021 ◽  
pp. 568-590
Author(s):  
James Davidson
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gaussian Processes ◽  
Variance Estimation ◽  
Limiting Distribution ◽  
Delta Method ◽  
Differentiable Functions ◽  
The Central Limit Theorem ◽  
Iterated Logarithm

This chapter contains treatments of a range of topics associated with the central limit theorem. These include estimated normalization using methods of heteroscedasticity and autocorrelation consistent variance estimation, the CLT in linear prrocesses, random norming giving rise to a mixed Gaussian limiting distribution, and the Cramér–Wold device and multivariate CLT. The delta method to derive the limit distributions of differentiable functions is described. The law of the iterated logarithm is proved for Gaussian processes.

Non-central limit theorem of the weighted power variations of Gaussian processes

2014 ◽  
Vol 43 (2) ◽  
pp. 215-223
Author(s):  
Iltae Kim ◽  
Hyun Suk Park ◽  
Yoon Tae Kim
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Gaussian Processes
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