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357
NONSTANDARD LIMIT THEOREM FOR INFINITE VARIANCE FUNCTIONALS
"... We consider functionals of longrange dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the longrange dependence is strong enough, the limit is a Hermite process, while for weaker longrange dependence, the limit is αstable Lévy motion. For the critica ..."
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Cited by 1 (0 self)
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We consider functionals of longrange dependent Gaussian sequences with infinite variance and obtain nonstandard limit theorems. When the longrange dependence is strong enough, the limit is a Hermite process, while for weaker longrange dependence, the limit is αstable Lévy motion
On Estimating the Intensity of LongRange Dependence in Finite and Infinite Variance Time Series
, 1996
"... The goal of this paper is to provide benchmarks to the practitioner for measuring the intensity of longrange dependence in time series. It provides a detailed comparison of eight estimators for longrange dependence, using simulated FARIMA(p; d; q) time series with different finite and infinite var ..."
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Cited by 63 (4 self)
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, the use of infinite variance instead of finite variance innovations does not cause a great dec...
Occupation time fluctuation limits of infinite variance equilibrium branching systems
, 2008
"... We establish limit theorems for the fluctuations of the rescaled occupation time of a (d, α, β)branching particle system. It consists of particles moving according to a symmetric αstable motion in R d. The branching law is in the domain of attraction of a (1+β)stable law and the initial condition ..."
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Cited by 3 (2 self)
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We establish limit theorems for the fluctuations of the rescaled occupation time of a (d, α, β)branching particle system. It consists of particles moving according to a symmetric αstable motion in R d. The branching law is in the domain of attraction of a (1+β)stable law and the initial
Clustering and Invariant Measures for Spatial Branching Models with Infinite Variance
, 1997
"... We consider two spatial branching models on R d : branching Brownian motion with a branching law in the domain of normal attraction of a (1 + fi) stable law, 0 ! fi 1, and the corresponding high density limit measure valued diffusion. The longtime behaviour of both models depends highly on fi and ..."
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Cited by 12 (2 self)
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We consider two spatial branching models on R d : branching Brownian motion with a branching law in the domain of normal attraction of a (1 + fi) stable law, 0 ! fi 1, and the corresponding high density limit measure valued diffusion. The longtime behaviour of both models depends highly on fi
Stable limits for sums of dependent infinite variance random variables
 PROBAB. THEORY RELAT. FIELDS
, 2010
"... ..."
A long range dependence stable process and an infinite variance branching system
 Ann. Probab. 35, No 2 (2007). Math. ArXiv PR/0511739
"... We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d,α,β)branching particle system (particles moving in R d according to a symmetric αstable Lévy process, branching law in the domain of attraction of a (1 + β)stable law, 0 < β < 1, uniform Poisson initial ..."
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Cited by 15 (7 self)
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We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d,α,β)branching particle system (particles moving in R d according to a symmetric αstable Lévy process, branching law in the domain of attraction of a (1 + β)stable law, 0 < β < 1, uniform Poisson
Bayesian Inference for Time series with Infinite Variance Stable Innovations
, 1998
"... This article describes the use of sampling based Bayesian inference for infinite variance stable distributions and for time series with infinite variance stable innovations. For time series, an advantage of the Bayesian approach is that it enables the simultaneous estimation of the parameters charac ..."
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Cited by 6 (0 self)
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This article describes the use of sampling based Bayesian inference for infinite variance stable distributions and for time series with infinite variance stable innovations. For time series, an advantage of the Bayesian approach is that it enables the simultaneous estimation of the parameters
Results 1  10
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357