Volatility occupation times

We propose nonparametric estimators of the occupation measure and the occupation density of the diffusion coefficient (stochastic volatility) of a discretely observed It\^{o} semimartingale on a fixed interval when the mesh of the observation grid shrinks to zero asymptotically. In a first step we estimate the volatility locally over blocks of shrinking length, and then in a second step we use these estimates to construct a sample analogue of the volatility occupation time and a kernel-based estimator of its density. We prove the consistency of our estimators and further derive bounds for their rates of convergence. We use these results to estimate nonparametrically the quantiles associated with the volatility occupation measure.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1135 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Disability and Occupation

[Excerpt] It is well-documented that people with disabilities have a significantly lower rate of employment than people without disabilities (36% versus 74% according to the 2006 American Community Survey (ACS)). Less is known about the types of work they do. Using the occupational classification system within the ACS, researchers explored the prevalence of people with disabilities within occupational groupings and discuss its relationship to occupational growth1. Future analysis will address variation across disability groups

Giving credit where it's due

Discusses the entitlement to occupation rent where one party to a relationship no longer lives in the matrimonial or family home in which he/she has an interest and a right of occupation. Describes the case law illustrating that forceful exclusion of the non-occupying party is not a prerequisite to entitlement to an occupation rent. Considers the calculation of the parties' respective credits where the occupying party has made mortgage repayments since the separation and the other is entitled to an occupation rent

Occupation Times for Jump Processes

We consider a class of pure jump Markov processes in \rr^d whose jump kernels are comparable to those of symmetric stable processes. We prove a support theorem, a lower bound on the occupation times of sets, and show that we can approximate resolvents using smooth functions