Exponential ergodicity of the jump-diffusion CIR process

In this paper we study the jump-diffusion CIR process (shorted as JCIR), which is an extension of the classical CIR model. The jumps of the JCIR are introduced with the help of a pure-jump L\'evy process $(J_t, t \ge 0)$. Under some suitable conditions on the L\'evy measure of $(J_t, t \ge 0)$, we derive a lower bound for the transition densities of the JCIR process. We also find some sufficient condition guaranteeing the existence of a Forster-Lyapunov function for the JCIR process, which allows us to prove its exponential ergodicity.Comment: 14 page

Examining the Association Between Well Child Care and Developmental and Behavioral Health Conditions in Children

Background: Well child care visits (WCC) are critical preventive care visits that start at infancy. Currently, little is known about the association between WCC and parent report of developmental and behavioral health conditions in children. The purpose of this research was to examine if WCC contributes to developmental/behavioral health conditions reported by parents. Methods: The 2016 National Health Interview Survey data were used for this research. Weighted estimates were calculated to assess the relationship between the receipt of WCC (yes or no response to receiving WCC in past 12 months) and presence of developmental/behavioral conditions; a Pearson’s chi square was used to determine bivariate associations between characteristics and WCC, followed by multivariable logistic regression to adjust for child sex, child age, healthcare access of parents, parent education level and parent income level. Results: Among 2,453 children 3 years and younger 91.04% of these children had received WCC in the past 12 months. The weighted percent of children with any developmental/behavioral conditions was 7.78% in those receiving WCC and 4.62% in children not receiving WCC. Bivariate associations determined that the statistically significant characteristics for determining whether a child receives WCC are: the child’s race/ethnicity, the number of office visits to their primary care (which are a combination of WCC and sick child visits), parent education level, and combined family income level. The logistic regression model evaluating developmental and behavioral conditions adjusted for these variables that were statistically significant. In the adjusted model it was found that the number of office visits and parent education level were statistically significant in the detection of developmental and behavioral health conditions. Conclusion: The number of office visits (which include WCC) are important preventive clinical services for identifying developmental/behavioral conditions in young children. Parent education level is another significant factor that determines receipt of WCC and detection of developmental/behavioral conditions. By understanding the factors associated with WCC, targeted interventions can be developed to increase identification of developmental/behavioral conditions

Zap Q-Learning for Optimal Stopping Time Problems

The objective in this paper is to obtain fast converging reinforcement learning algorithms to approximate solutions to the problem of discounted cost optimal stopping in an irreducible, uniformly ergodic Markov chain, evolving on a compact subset of $\mathbb{R}^n$. We build on the dynamic programming approach taken by Tsitsikilis and Van Roy, wherein they propose a Q-learning algorithm to estimate the optimal state-action value function, which then defines an optimal stopping rule. We provide insights as to why the convergence rate of this algorithm can be slow, and propose a fast-converging alternative, the "Zap-Q-learning" algorithm, designed to achieve optimal rate of convergence. For the first time, we prove the convergence of the Zap-Q-learning algorithm under the assumption of linear function approximation setting. We use ODE analysis for the proof, and the optimal asymptotic variance property of the algorithm is reflected via fast convergence in a finance example

Invariant, super and quasi-martingale functions of a Markov process

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures

A new design concept for indraft wind-tunnel inlets with application to the national full-scale aerodynamic complex

The present inlet design concept for an indraft wind tunnel, which is especially suited to applications for which a specific test section flow quality is required with minimum inlet size, employs a cascade or vaneset to control flow at the inlet plane, so that test section total pressure variation is minimized. Potential flow panel methods, together with empirical pressure loss predictions, are used to predict inlet cascade performance. This concept has been used to develop an alternative inlet design for the 80 x 120-ft wind tunnel at NASA Ames Research Center. Experimental results show that a short length/diameter ratio wind tunnel inlet furnishing atmospheric wind isolation and uniform test section flow can be designed

Deoxyribonucleic Acid Synthesis in Ultraviolet-Light-Irradiated Chinese Hamster Cells

Two mammalian cell lines, Chinese hamster ovary (CHO) which can recover colony-forming ability between fractionated doses of ultraviolet light (UV), and Chinese hamster B-14FAF28 which cannot recover, were tested for the ability to bypass UV-induced photoproducts in DNA during postirradiation DNA synthesis. The molecular weight distributions of newly synthesized DNA in UV-irradiated populations of both cell lines showed evidence for photoproduct bypass. Hence, the bypass mechanism does not correlate with recovery after UV