We construct and investigate a (1−α)-upper prediction bound for a future observation of a cyclic Poisson process using past data. A normal based confidence interval for our upper prediction bound is established. A comparison of the new prediction bound with a simpler nonparametric prediction...

In the present paper, we propose a Palm likelihood approach as a general estimating principle for stationary point processes in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbf{R}^d$$</EquationSource> </InlineEquation> for which the density of the second-order factorial moment measure is available in closed form or in an integral representation. Examples of such...</equationsource></inlineequation>

We study the problem of parameter estimation for Ornstein–Uhlenbeck processes driven by symmetric α-stable motions, based on discrete observations. A least squares estimator is obtained by minimizing a contrast function based on the integral form of the process. Let h be the length of time...