Displaying similar documents to “An application of multivariate total positivity to peacocks”

Expansions for Repeated Integrals of Products with Applications to the Multivariate Normal

Christopher S. Withers, Saralees Nadarajah (2011)

ESAIM: Probability and Statistics

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We extend Leibniz' rule for repeated derivatives of a product to multivariate integrals of a product. As an application we obtain expansions for ( < < ) for ~ (0,) and for repeated integrals of the density of . When > 0 in the expansion for ( < ) reduces to one given by [H. Ruben B 68 (1964) 3–11]. in terms of the moments of (0, ). This is shown to be a special case of an expansion...

Expansions for Repeated Integrals of Products with Applications to the Multivariate Normal

Christopher S. Withers, Saralees Nadarajah (2012)

ESAIM: Probability and Statistics

Similarity:

We extend Leibniz' rule for repeated derivatives of a product to multivariate integrals of a product. As an application we obtain expansions for ( < < ) for ~ (0,) and for repeated integrals of the density of . When > 0 in the expansion for ( < ) reduces to one given by [H. Ruben B (1964) 3–11]. in terms of the moments of (0, ). This is shown to be a special case of an expansion in terms...

Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory

Elena Di Bernardino, Thomas Laloë, Véronique Maume-Deschamps, Clémentine Prieur (2013)

ESAIM: Probability and Statistics

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This paper deals with the problem of estimating the level sets () =  {() ≥ }, with  ∈ (0,1), of an unknown distribution function on ℝ . A plug-in approach is followed. That is, given a consistent estimator of , we estimate () by () =  { () ≥ }. In our setting, non-compactness property is required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric...

Linear diffusion with stationary switching regime

Xavier Guyon, Serge Iovleff, Jian-Feng Yao (2010)

ESAIM: Probability and Statistics

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Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other...

The law of the iterated logarithm for the multivariate kernel mode estimator

Abdelkader Mokkadem, Mariane Pelletier (2010)

ESAIM: Probability and Statistics

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Let be the mode of a probability density and its kernel estimator. In the case is nondegenerate, we first specify the weak convergence rate of the multivariate kernel mode estimator by stating the central limit theorem for . Then, we obtain a multivariate law of the iterated logarithm for the kernel mode estimator by proving that, with probability one, the limit set of the sequence suitably normalized is an ellipsoid. We also give a law of the iterated logarithm for the norms,...

Meeting time of independent random walks in random environment

Christophe Gallesco (2013)

ESAIM: Probability and Statistics

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We consider, in the continuous time version, independent random walks on Z in random environment in Sinai’s regime. Let be the first meeting time of one pair of the random walks starting at different positions. We first show that the tail of the quenched distribution of , after a suitable rescaling, converges in probability, to some functional of the Brownian motion. Then we compute the law of this functional. Eventually, we obtain results about the...

On ℝd-valued peacocks

Francis Hirsch, Bernard Roynette (2013)

ESAIM: Probability and Statistics

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In this paper, we consider ℝ-valued integrable processes which are increasing in the convex order, ℝ-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝ-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝ-valued martingale. This extends former results, obtained notably by Strassen [36 (1965) 423–439], Doob [2 (1968) 207–225] and Kellerer [198 (1972) 99–122].

Survival probabilities of autoregressive processes

Christoph Baumgarten (2014)

ESAIM: Probability and Statistics

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Given an autoregressive process of order (  =   + ··· +   +  where the random variables , ,... are i.i.d.), we study the asymptotic behaviour of the probability that the process does not exceed a constant barrier up to time (survival or persistence probability). Depending on the coefficients ,...,...

On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case

Sara Brofferio, Dariusz Buraczewski, Ewa Damek (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We consider the autoregressive model on ℝ defined by the stochastic recursion = −1 + , where {( , )} are i.i.d. random variables valued in ℝ× ℝ+. The critical case, when 𝔼 [ log A 1 ] = 0 , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measure for the Markov chain { }. In the present paper we prove that the weak limit of properly...