Dimension free and infinite variance tail estimates on Poisson space
نویسندگان
چکیده
Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including Lévy’s stochastic area and the square norm of Brownian paths. In the infinite variance case, various tail estimates such as stable ones are also presented.
منابع مشابه
Estimation of AR Parameters in the Presence of Additive Contamination in the Infinite Variance Case
If we try to estimate the parameters of the AR process {Xn} using the observed process {Xn+Zn} then these estimates will be badly biased and not consistent but we can minimize the damage using a robust estimation procedure such as GM-estimation. The question is does additive contamination affect estimates of “core” parameters in the infinite variance case to the same extent that it does in the ...
متن کاملTail Behavior of Random Products and Stochastic Exponentials
In this paper we study the distributional tail behavior of the solution to a linear stochastic differential equation driven by infinite variance α-stable Lévy motion. We show that the solution is regularly varying with index α. An important step in the proof is the study of a Poisson number of products of independent random variables with regularly varying tail. The study of these products dese...
متن کاملOn the spread of a branching Brownian motion whose offspring number has infinite variance
We study the impact on shape parameters of an underlying Bienaymé-Galton-Watson branching process (height, width and first hitting time), of having a non-spatial branching mechanism with infinite variance. Aiming at providing a comparative study of the spread of an epidemics whose dynamics is given by the modulus of a branching Brownian motion (BBM) we then consider spatial branching processes ...
متن کاملUnit Root Inference for Non-Stationary Linear Processes driven by Infinite Variance Innovations∗
The contribution of this paper is two-fold. First, we derive the asymptotic null distribution of the familiar augmented Dickey-Fuller [ADF] statistics in the case where the shocks follow a linear process driven by infinite variance innovations. We show that these distributions are free of serial correlation nuisance parameters but depend on the tail index of the infinite variance process. These...
متن کاملBayesian Analysis of Stochastic Volatility Models with Levy Jumps: Application to Value at Risk
In this paper we analyze asset returns models with diffusion part and jumps in returns with stochastic volatility either from diffusion or pure jump part. We consider different specifications for the pure jump part including compound Poisson, Variance Gamma and Levy α-stable jumps. Monte Carlo Markov chain algorithm is constructed to estimate models with latent Variance Gamma and Levy α−stable ...
متن کامل