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Asymptotics of Predictive Distributions
2016Let \((X_n)\) be a sequence of random variables, adapted to a filtration \((\mathcal {G}_n)\), and let \(\mu _n=(1/n)\,\sum _{i=1}^n\delta _{X_i}\) and \(a_n(\cdot )=P(X_{n+1}\in \cdot \mid \mathcal {G}_n)\) be the empirical and the predictive measures. We focus on \(||\mu _n-a_n||=\sup _{B\in \mathcal {D}}\,|\mu _n(B)-a_n(B)|\), where \(\mathcal {D}\)
Patrizia Berti +2 more
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Asymptotic Exit Time Distributions
SIAM Journal on Applied Mathematics, 1982Let $x( t )$ be a diffusion resulting from the stochastic perturbation of a deterministic dynamical system by a nondegenerate white noise. Let $\tau $ be the time of first exit of $x( t )$ from a domain on which the deterministic flow has a single simple attracting critical point and is inward at the boundary.
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ASYMPTOTIC DISTRIBUTION OF EIGENVALUES
Mathematics of the USSR-Izvestiya, 1983The method of a spectral almost-projection is employed to investigate the asymptotic behavior of the eigenvalue distribution functions of semibounded essentially selfadjoint systems of differential operators in a domain and of pseudodifferential operators on Rn.
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Asymptotic expansions for probability distributions. II
Lithuanian Mathematical Journal, 1983[For part III see the foregoing review; Zbl 0571.60033.] Let \(\xi\) be a lattice random variable on \(\{\) 0,1,2,...\(\}\) with the probability distribution p(k). It is assumed that the cumulants \(\gamma_{\ell}\) of order \(\ell =1,2,..\). satisfy the conditions: \(\gamma_ 1>0,| \gamma_{\ell}| \leq Hc^{\ell}\ell !/\Delta^{\ell -1}\), \(\ell =2,3,..\).
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Local Asymptotic Distributions of Stationarity Tests
Journal of Time Series Analysis, 2006Abstract. In this paper, we study the asymptotic behaviour of several test statistics of the null hypothesis of stationarity under a sequence of local alternatives. The sequence of local alternatives is modelled as a nearly stationary process, i.e. a non‐stationary process in any finite sample which converges to a stationary process asT ↑ ∞.
CAPPUCCIO, NUNZIO, LUBIAN D.
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S-asymptotic of a distribution
Pliska. Studia Mathematica Bulgarica, 1989Summary: We give a definition of asymptotic behaviour at infinity of a Schwartz distribution -- the so-called S-asymptotic. Some basic properties of this S-asymptotic are proved and possibilities of its applications are given.
Pilipović, Stevan, Stanković, Bogoljub
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Asymptotically Optimal Distributed Censoring
2006 IEEE International Symposium on Information Theory, 2006We consider the problem of Bayesian decentralized binary detection in a sensor network in which the sensors have access to some side information that affects the statistics of the measurements they make. Sensors can decide whether or not to make a measurement and transmit a message to the fusion center ("censoring"), and also have a choice of the ...
Wee-peng Tay, John Tsitsiklis, Moe Win
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Asymptotic distributions of pontograms
Mathematical Proceedings of the Cambridge Philosophical Society, 1987Let{N(x), x ≥ 0} be a Poisson process with intensity parameter λ > 0, and introduceWhen looking for the changepoint in the Land's End data, Kendall and Kendall [7] proved for all 0 < ε1 < 1 − ε2 < 1 thatwhere {V(s), − ∞ < s < ∞} is an Ornstein–Uhlenbeck process with covariance function exp (−|t − s|). D. G.
Csörgö, Miklós, Horváth, Lajos
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Asymptotically almost periodic distributions
Applicable Analysis, 1989In this work we extend to the space of Schwartz' distributions the notion of asymptotic almost periodicity of M. Frechet. The main justification for the introduction of this concept is the fact that for certain differential equations in distributions the existence of an asymptotic almost periodic (distribution) solution implies the existence of an ...
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