Occupation Densities

Occupation times and Bessel densities

Consider a Markov process with countably many states. In order to find a one-state occupation time distribution, we use a combination of Fourier and Laplace transforms in the way that allows for the inversion of the Fourier transform. We derive a closed-form expression for the occupation time distribution in the case of a simple continuous time random walk on Z and represent the one state occup...

Occupation densities for certain processes related to fractional Brownian motion

In this paper we establish the existence of a square integrable occupation density for two classes of stochastic processes. First we consider a Gaussian process with an absolutely continuous random drift, and secondly we handle the case of a (Skorohod) integral with respect to the fractional Brownian motion with Hurst parameter H > 1 2 . The proof of these results uses a general criterion for t...

Occupation Therapy

Densities, spectral densities and modality

This paper considers the problem of specifying a simple approximating density function for a given data set (x1, . . . , xn). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The taut string method is used to control the numbers of modes and to produce candidate approximating densities. Refinements are introduced that improve the l...

Occupation groups and Covid-19