Inverse Gaussian Ornstein-Uhlenbeck Stochastic Clocks

In this pose, we consider an Ornstein-Uhlenbeck stochastic clock whose instantaneous rate of activity process has an inverse Gaussian stationary distribution. We use the previously obtained relationship between the cumulant generation function of the stationary distribution and that of the background driving Lévy process and show that the latter can be represented as the sum of an inverse Gaussian processes and a compound Poisson process with chi-squared distributed increments.

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