Maximum Likelihood Estimator for Hidden Markov Models in continuous time

The paper studies large sample asymptotic properties of the Maximum Likelihood Estimator (MLE) for the parameter of a continuous time Markov chain, observed in white noise. Using the method of weak convergence of likelihoods due to I.Ibragimov and R.Khasminskii, consistency, asymptotic normality and convergence of moments are established for MLE under certain strong ergodicity conditions of the chain.Comment: Warning: due to a flaw in the publishing process, some of the references in the published version of the article are confuse

Continuity and anomalous fluctuations in random walks in dynamic random environments: numerics, phase diagrams and conjectures

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random walks. We observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment. We compare our data with well known results for static random environment. We observe that the non-diffusive regime known so far only for the static case can occur in the dynamic setup too. Such anomalous fluctuations give rise to a new phase diagram. Further we discuss possible consequences for more general static and dynamic random environments.Comment: 33 pages, 23 figure

1-Year Mortality and Surgery Incidence in Older US Adults with Cervical Spine Fracture

Background: Traumatic cervical spinal cord injuries (SCIs) can be lethal and are especially dangerous for older adults. Falls from standing and risk factors for a cervical fracture and spinal cord injury increase with age. This study estimates the 1-year mortality for patients with a cervical fracture and resultant SCI and compares the mortality rate with that from an isolated cervical fracture. Methods: We performed a retrospective cohort study of U.S. Medicare patients older than 65 years of age. International Classification of Diseases (ICD)-9 codes were used to identify patients with a cervical fracture without SCI and patients with a cervical fracture with SCI between 2007 and 2014. Our primary outcome was 1-year mortality cumulative incidence rate; our secondary outcome was the cumulative incidence rate of surgical intervention. Propensity weighted analysis was performed to balance covariates between the groups. Results: The SCI cohort had a 1-year mortality of 36.5%, compared with 31.1% in patients with an isolated cervical fracture (risk difference 5.4% (2.9%–7.9%)). Patients with an SCI were also more likely to undergo surgical intervention compared with those without a SCI (23.1% and 10.3%, respectively; risk difference 12.8% (10.8%-14.9%)). Conclusions: Using well-adjusted population-level data in older adults, this study estimates the 1-year mortality after SCI in older adults to be 36.5%. The mortality after a cervical fracture with SCI was 5 percentage points higher than in patients without SCI, and this difference is smaller than one might expect, likely representing the frailty of this population and unmeasured covariates

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

Cut Points and Diffusions in Random Environment

In this article we investigate the asymptotic behavior of a new class of multi-dimensional diffusions in random environment. We introduce cut times in the spirit of the work done by Bolthausen, Sznitman and Zeitouni, see [4], in the discrete setting providing a decoupling effect in the process. This allows us to take advantage of an ergodic structure to derive a strong law of large numbers with possibly vanishing limiting velocity and a central limit theorem under the quenched measure.Comment: 44 pages; accepted for publication in "Journal of Theoretical Probability

Random walks in space time mixing environments

We prove that random walks in random environments, that are exponentially mixing in space and time, are almost surely diffusive, in the sense that their scaling limit is given by the Wiener measure.Comment: 28 page

Photodynamic therapy for multi-resistant cutaneous Langerhans cell histiocytosis

Langerhans cell histiocytosis is a rare group of proliferative disorders. Beside cutaneous involvement, other internal organs can be affected. The treatment of cutaneous lesions is difficult and relies on topical corticosteroids, carmustine, nitrogen mustard, and photochemotherapy. Systemic steroids and vinblastine are used for recalcitrant skin lesions. However, some cases fail to respond. An 18-month old boy presented a CD1a+, S100a+ Langerhans cell histocytosis with cutaneous and severe scalp involvement. Topical corticosteroids and nitrogen mustard failed to improve the skin lesions. Systemic corticosteroids and vinblastine improved the truncal involvement but had no effect on the scalp lesions. Methylaminolevulinate (MAL) based photodynamic therapy (PDT) resulted in a significant regression of the scalp lesions. Control histology revealed an almost complete clearance of the tumor infiltrate. Clinical follow-up after six months showed no recurrence