An Inverse Gamma Activity Time Process with Noninteger Parameters and a Self-Similar Limit

Finlay, Richard; Seneta, E.; Wang, Dingcheng

doi:10.1017/s0021900200009190

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…Familiar special cases of second‐order Lévy processes are Brownian motion, Poisson process, negative binomial process, gamma process, inverse Gaussian process, normal inverse Gaussian process (Barndorff‐Nielsen ()), inverse Gamma process (Finlay et al ()), variance Gamma process (Madan & Seneta (), Finlay & Seneta ()) and second‐order Student process (Heyde & Leonenko ()). Simulation procedures of these Lévy processes are available in the literature (e.g., Schoutens (), Webber () and Sorensen & Benth ()) and make it possible to simulate the process .…”

Section: Construction Of Stationary Process With Pólya‐type Covariancmentioning

confidence: 99%

Vector Stochastic Processes with Pólya‐Type Correlation Structure

2016

Int Statistical Rev

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Summary This paper introduces a simple method to construct a stationary process on the real line with a Pólya‐type covariance function and with any infinitely divisible marginal distribution, by randomising the timescale of the increment of a second‐order Lévy process with an appropriate positive random variable. With the construction method extended to the multivariate case, we construct vector stochastic processes with Pólya‐type direct covariance functions and with any specified infinitely divisible marginal distributions. This makes available a new class of non‐Gaussian vector stochastic processes with flexible correlation structure for use in modelling and simulation.

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Section: Construction Of Stationary Process With Pólya‐type Covariancmentioning

confidence: 99%

Vector Stochastic Processes with Pólya‐Type Correlation Structure

2016

Int Statistical Rev

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Isotropic random fields with infinitely divisible marginal distributions

Wang

Leonenko

2017

Stochastic Analysis and Applications

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A simple but efficient approach is proposed in this paper to construct the isotropic random field in R d (d ≥ 2), whose univariate marginal distributions may be taken as any infinitely divisible distribution with finite variance. The three building blocks in our building tool box are a second-order Lévy process on the real line, a d-variate random vector uniformly distributed on the unit sphere, and a positive random variable that generates a Pólya-type function. The approach extends readily to the multivariate case and results in a vector random field in R d with isotropic direct covariance functions and with any specified infinitely divisible marginal distributions. A characterization of the turning bands simulation feature is also derived for the covariance matrix function of a Gaussian or elliptically contoured random field that is isotropic and mean square continuous in R d .

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An Inverse Gamma Activity Time Process with Noninteger Parameters and a Self-Similar Limit

Cited by 2 publications

References 11 publications

Vector Stochastic Processes with Pólya‐Type Correlation Structure

Vector Stochastic Processes with Pólya‐Type Correlation Structure

Isotropic random fields with infinitely divisible marginal distributions

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