QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

Etiological and Clinical Features of Childhood Psychotic Symptoms Results From a Birth Cohort

Context: It has been reported that childhood psychotic symptoms are common in the general population and may signal neurodevelopmental processes that lead to schizophrenia. However, it is not clear whether these symptoms are associated with the same extensive risk factors established for adult schizophrenia. Objective: To examine the construct validity of children`s self-reported psychotic symptoms by testing whether these symptoms share the risk factors and clinical features of adult schizophrenia. Design: Prospective, longitudinal cohort study of a nationally representative birth cohort in Great Britain. Participants: A total of 2232 twelve-year-old children followed up since age 5 years ( retention, 96%). Main Outcome Measure: Children`s self-reported hallucinations and delusions. Results: Children`s psychotic symptoms are familial and heritable and are associated with social risk factors (eg, urbanicity); cognitive impairments at age 5; home-rearing risk factors ( eg, maternal expressed emotion); behavioral, emotional, and educational problems at age 5; and comorbid conditions, including self-harm. Conclusions: The results provide a comprehensive picture of the construct validity of children`s self-reported psychotic symptoms. For researchers, the findings indicate that children who have psychotic symptoms can be recruited for neuroscience research to determine the pathogenesis of schizophrenia. For clinicians, the findings indicate that psychotic symptoms in childhood are often a marker of an impaired developmental process and should be actively assessed.