On the approximation of an integral by a sum of random variables.

Einmahl, John H.J.; Van Zuijlen, Martien C.A.

Displaying similar documents to “On the approximation of an integral by a sum of random variables.”

Limit theorems for U-statistics indexed by a one dimensional random walk

Nadine Guillotin-Plantard, Véronique Ladret (2005)

ESAIM: Probability and Statistics

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Let ${(S_{n})}_{n \geq 0}$ be a $ℤ$ -random walk and ${(ξ_{x})}_{x \in ℤ}$ be a sequence of independent and identically distributed $ℝ$ -valued random variables, independent of the random walk. Let $h$ be a measurable, symmetric function defined on $ℝ^{2}$ with values in $ℝ$ . We study the weak convergence of the sequence $𝒰_{n}, n \in ℕ$ , with values in $D [0, 1]$ the set of right continuous real-valued functions with left limits, defined by $\sum_{i, j = 0}^{[n t]} h (ξ_{S_{i}}, ξ_{S_{j}}), t \in [0, 1] .$ Statistical applications are presented, in particular we prove a strong law of large numbers for...

$L^{1}$ -norm of infinitely divisible random vectors and certain stochastic integrals.

Marcus, Michael B., Rosiński, Jan (2001)

Electronic Communications in Probability [electronic only]

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Logarithmic information of degree $q$ linked with an extension of Fisher’s information

Bernadette Bouchon, Franquiberto Pessoa (1985)

Kybernetika

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Large deviations for independent random variables – Application to Erdös-Renyi’s functional law of large numbers

Jamal Najim (2005)

ESAIM: Probability and Statistics

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A Large Deviation Principle (LDP) is proved for the family $\frac{1}{n} \sum_{1}^{n} 𝐟 (x_{i}^{n}) \cdot Z_{i}^{n}$ where the deterministic probability measure $\frac{1}{n} \sum_{1}^{n} δ_{x_{i}^{n}}$ converges weakly to a probability measure $R$ and ${(Z_{i}^{n})}_{i \in ℕ}$ are $ℝ^{d}$ -valued independent random variables whose distribution depends on $x_{i}^{n}$ and satisfies the following exponential moments condition: $sup_{i, n} 𝔼 e^{α^{*} | Z_{i}^{n} |} < + \infty forsome 0 < α^{*} < + \infty .$ In this context, the identification of the rate function is non-trivial due to the absence of equidistribution. We rely on fine convex analysis to address this issue. Among...

Grüss-type bounds for the covariance of transformed random variables.

Egozcue, Martín, García, Luis Fuentes, Wong, Wing-Keung, Zitikis, Ričardas (2010)

Journal of Inequalities and Applications [electronic only]

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Limit distributions for the ratio of the random sum of squares to the square of the random sum with applications to risk measures.

Ladoucette, Sophie A., Teugels, Jef J. (2006)

Publications de l'Institut Mathématique. Nouvelle Série

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Dominant eigenvalue problem for positive integral operators and its solution by Monte Carlo method

Jan Kyncl (1998)

Applications of Mathematics

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In this paper, a method of numerical solution to the dominant eigenvalue problem for positive integral operators is presented. This method is based on results of the theory of positive operators developed by Krein and Rutman. The problem is solved by Monte Carlo method constructing random variables in such a way that differences between results obtained and the exact ones would be arbitrarily small. Some numerical results are shown.

Tail behaviour of multiple random integrals and $U$ -statistics.

Major, Péter (2005)

Probability Surveys [electronic only]

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About the Lindeberg method for strongly mixing sequences

Emmanuel Rio (1997)

ESAIM: Probability and Statistics

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