Results 11  20
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357
A limit theorem for weighted sums of infinite variance random variables with longrange dependence,
, 2003
"... Abstract. Let {ξ j } j∈Z be a sequence of random variables which belong to the domain of attraction of a linear fractional stable motion {∆ H,α (t)} with infinite variance. We study the convergence of weighted sums (u) in distribution under suitable assumptions on a class of deterministic function ..."
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Cited by 1 (0 self)
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Abstract. Let {ξ j } j∈Z be a sequence of random variables which belong to the domain of attraction of a linear fractional stable motion {∆ H,α (t)} with infinite variance. We study the convergence of weighted sums (u) in distribution under suitable assumptions on a class of deterministic
Linear prediction of ARMA processes with infinite variance
 Stochastic Proc. Appl
, 1985
"... In order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale paramet ..."
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Cited by 8 (0 self)
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In order to predict unobserved values of a linear process with infinite variance, we introduce a linear predictor which minimizes the dispersion (suitably defined) of the error distribution. When the linear process is driven by symmetric stable white noise this predictor minimizes the scale
Nonparametric Regression Under Dependent Errors With Infinite Variance
"... We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic li ..."
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Cited by 4 (0 self)
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We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic
PORTMANTEAU TESTS FOR ARMA MODELS WITH INFINITE VARIANCE
, 2006
"... Autoregressive and movingaverage (ARMA) models with stable Paretian errors are some of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem of diagnostic checking of fitted models has not been addre ..."
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Cited by 1 (0 self)
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Autoregressive and movingaverage (ARMA) models with stable Paretian errors are some of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem of diagnostic checking of fitted models has not been
Limit Theorems For Continuous Time Random Walks With Infinite Mean Waiting Times
 JOURNAL OF APPLIED PROBABILITY
, 2003
"... A continuous time random walk is a simple random walk subordinated to a renewal process, used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Levy motion subordinated to the hitting time process o ..."
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Cited by 72 (34 self)
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A continuous time random walk is a simple random walk subordinated to a renewal process, used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Levy motion subordinated to the hitting time process
The Variance Ratio Test with Stable Paretian Errors
, 2000
"... In this paper we examine the distribution of the variance ratio statistic when the errors are distributed with thick tails as described by the family of stable Paretian distributions. The asymptotic distribution of the OVR statistic, which depends on the characteristic exponent, can be estimated usi ..."
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Cited by 2 (0 self)
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In this paper we examine the distribution of the variance ratio statistic when the errors are distributed with thick tails as described by the family of stable Paretian distributions. The asymptotic distribution of the OVR statistic, which depends on the characteristic exponent, can be estimated
ON BESOV REGULARITY OF BROWNIAN MOTIONS IN INFINITE DIMENSIONS
, 801
"... Abstract. We extend to the vectorvalued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion. We also consider a Brownian motion as a Besov space valued random variable. It turns out that a Brownian motion, in this interpretati ..."
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Cited by 8 (4 self)
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Abstract. We extend to the vectorvalued situation some earlier work of Ciesielski and Roynette on the Besov regularity of the paths of the classical Brownian motion. We also consider a Brownian motion as a Besov space valued random variable. It turns out that a Brownian motion
WEAK CONVERGENCE OF THE FUNCTIONINDEXED INTEGRATED PERIODOGRAM FOR INFINITE VARIANCE PROCESSES
, 2009
"... Abstract. In this paper we study the weak convergence of the integrated periodogram indexed by classes of functions for linear and stochastic volatility processes with symmetric αstable noise. Under suitable summability conditions on the series of the Fourier coefficients of the index functions we ..."
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Cited by 3 (2 self)
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show that the weak limits constitute αstable processes which have representation as infinite Fourier series with iid αstable coefficients. The cases α ∈ (0, 1) and α ∈ [1, 2) are dealt with by rather different methods and under different assumptions on the classes of functions. For example
JP4.9 OBSERVATIONS OF VELOCITY VARIANCE IN THE STABLE BOUNDARY LAYER
"... Current atmospheric models underrepresent mesoscale motions in the stable boundary layer. Such motions have been referred to as meandering, although the source of these motions is usually not ..."
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Current atmospheric models underrepresent mesoscale motions in the stable boundary layer. Such motions have been referred to as meandering, although the source of these motions is usually not
(14/11/2005) A LONG RANGE DEPENDENCE STABLE PROCESS AND AN INFINITE VARIANCE BRANCHING SYSTEM ∗
"... We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, α, β)branching particle system (particles moving in Rd 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 init ..."
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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 Rd 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
Results 11  20
of
357